U.S. patent application number 11/624470 was filed with the patent office on 2007-07-19 for means and methods for construction and use of geodesic rhombic triacontahedron.
Invention is credited to David Glenn Henderson, Michael Thompson Morley.
Application Number | 20070163185 11/624470 |
Document ID | / |
Family ID | 38261803 |
Filed Date | 2007-07-19 |
United States Patent
Application |
20070163185 |
Kind Code |
A1 |
Morley; Michael Thompson ;
et al. |
July 19, 2007 |
Means and methods for construction and use of geodesic rhombic
triacontahedron
Abstract
A structural system comprising the symmetrical interpenetration
of an icosahedron and dodecahedron, further articulated to form a
rhombic triacontahedron with each rhombus subdivided by two
diagonals at its midpoint. The vertices of the original icosahedron
and dodecahedron, and the midpoints of the rhombi, are projected
such that a single circumscribed sphere would touch or nearly touch
all three sets of resulting vertices. This geometry may used to
create a hemispheric geodesic dome. Alternatively, this dome may be
subdivided along the hemisphere's great circle segments into two
half domes or four quarter domes. Rectangular structural elements
may be inserted between the half or quarter domes to increase dome
area without increasing dome height and to provide other
advantages. The basic triangular components of the disclosed
structure may be cut with minimal waste from conventional
rectangular construction material such as Structural Insulated
Panels. These basic triangular components may be connected with a
living hinge.
Inventors: |
Morley; Michael Thompson;
(Lawrence, KS) ; Henderson; David Glenn; (San
Rafael, CA) |
Correspondence
Address: |
STEVEN A. NIELSEN;ALLMAN & NIELSEN, P.C
100 Larkspur Landing Circle
Suite 212
LARKSPUR
CA
94939
US
|
Family ID: |
38261803 |
Appl. No.: |
11/624470 |
Filed: |
January 18, 2007 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
60760009 |
Jan 18, 2006 |
|
|
|
Current U.S.
Class: |
52/81.1 |
Current CPC
Class: |
E04B 7/102 20130101;
E04B 2001/3276 20130101; E04B 1/3211 20130101; E04B 1/3205
20130101; E04B 2001/3223 20130101; E04B 2001/3294 20130101 |
Class at
Publication: |
052/081.1 |
International
Class: |
E04B 7/08 20060101
E04B007/08 |
Claims
1. A building structure comprising a plurality of two sets of near
right angle component triangles, with each set a mirror image of
the other, such that the vertices of the structure are all of equal
radial distance from the center of the structure, thus creating a
structural approximation of a hemisphere with great circle segments
crossing at the apex of the hemisphere.
2. The building structure of claim 1 wherein the vertices
correspond to a subdivided rhombic triacontahedron such that
vertices of the original icosahedron, vertices of the original
dodecahedron, and the midpoints of the rhombic diagonals are
projected so that all three resulting sets of vertices are of equal
radial distance from the center of the structure.
3. The building structure of claim 2 wherein the vertices of the
original icosahedron, vertices of the original dodecahedron, and
the midpoints of the rhombic diagonals are of unequal radial
distance from the center of the structure but are close enough to
equal distance to produce near right angle component triangles
which can be cut efficiently (less than 15% material cutting waste)
from rectilinear building materials.
4. The building structure of claim 2 wherein the vertices of the
original icosahedron, vertices of the original dodecahedron, and
the midpoints of the rhombic diagonals are of unequal radial
distance from the center of the structure but are close enough to
equal distance to produce a close approximation of a hemisphere
with great circle segments crossing at the apex of the
hemisphere.
5. The building structure of claim 3 wherein the intersection
points of the rhombi diagonals are projected to a radial length
between the radius length of the icosahedron and the radius length
of the dodecahedron.
6. The hemisphere structure of claim 2 subdivided into two half
domes along either of the hemisphere's great circle segments.
7. The two half domes of claim 6 moved apart.
8. The two half domes of claim 7 with rectangular structural
elements inserted between the two half domes.
9. The two half domes of claim 6 subdivided into four quarter domes
along the remaining great circle segments of the original
hemisphere.
10. The four quarter domes of claim 9 moved apart.
11. The four quarter domes of claim 10 with rectangular structural
elements inserted between the four quarter domes.
12. The building structure of claim 1 constructed from structural
insulated panels (SiPs).
13. The building structure of claim 1 comprising a basic spherical
geometry comprising 62 vertices, 120 triangular faces and 180
edges, with all 120 triangular faces having the same angles and
size, with 60 of the triangular faces being mirror images of the
other 60 triangular faces.
14. The building structure of claim 12 wherein the triangular SIPs
are beveled.
15. The panels of claim 14 wherein each edge of a panel has a
different dihedral angle.
16. The panels of claim 15 wherein each edge of a triangular panel
is approximately 2 degrees, 20 degrees and 30 degrees.
17. The panels of claim 16 connected together with a spline
comprising a living hinge.
18. The spline of claim 17 fixed in three separate angles of
approximately 2 degrees, 20 degrees, and 31 degrees.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application claims the benefit of U.S. provisional
application "Geodesic triacontrahedron" application No. 60/760,009,
filed on Jan. 18, 2006 and is incorporated herein by reference.
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
[0002] Not Applicable
REFERENCE TO A SEQUENCE LISTING
[0003] Not Applicable
BACKGROUND OF THE INVENTION
[0004] (1) Field of the Invention
[0005] The invention relates to means and methods of combining two
platonic solids, the icosahedron and the dodecahedron, as a dual
geometry and further articulating this geometry to form a rhombic
triacontahedron with each rhombus subdivided by two diagonals at
its midpoint. The vertices of the original icosahedron and
dodecahedron, and the midpoints of the rhombi, are projected such
that a single circumscribed sphere touches or nearly touches all
three sets of resulting vertices. This geometry creates dome-like
dwelling designs with unique and useful connection and expansion
capabilities. The geometry's single basic triangular component
facilitates highly efficient panelized use of prefabricated
building materials such as Structural Insulated Panels (SIPs). The
invention also relates to means of creating a panel connection
system to secure the disclosed panels.
[0006] (2) Description of the Related Art
[0007] U.S. Pat. No. 5,628,154 to Gavette discloses a modular
system of constructing a spherical icosahedron or dodecahedron. The
Gavette dome may be viewed as a collection of pentagons, and deemed
a dodecahedron or may be viewed as a collection of triangles, and
deemed a hexakis icosahedron. In either case, the panels are
constructed as non-planar or curved segments of a sphere.
[0008] Gavette is not suited for the construction of dome segments
from conventional planar or flat surfaced construction components.
Gavette uses a plurality of right angle or near right angle
triangles formed in aggregate as large curved components.
Structural Insulated Panels (SIPs), sheets of plywood, and other
widely available and relatively inexpensive construction materials
are planar and hence not usable for construction of a Gavette
dome.
[0009] Gavette's integrated ribbing structure or support system
also makes Gavette unsuitable for efficient construction of larger
structures, Gavette requires curved support components built into
curved panels. These larger curved panels are inefficient for
efficient storage and shipment. Furthermore, the integrated rib
system of Gavette does not allow for the Gavette dome to easily and
efficiently integrate doors, windows and other standard building
components typical of full scale structures,
[0010] The preferred and illustrated embodiment of Gavette's dome
is an orientation of the basic icosahedron/dodecahedron dual
geometry that has ten triangles coming together at its apex. This
permits some separation and expansion but not the four way
separation and expansion possible with the disclosed design. In
addition, Gavette's preferred embodiment precludes a hemispheric
dome in favor of an approximate 5/8 dome. The inwardly curving
portion of this 5/8 dome near the base makes door and window
integration additionally problematic. This 5/8 embodiment, along
with his very large basic building components, make the Gavette
design efficiently suitable for only relatively small scale
structures.
[0011] Thus, there is a need in the art for means to construct
relatively large, full scale dome structures from flat construction
stock and to integrate conventional building components such as
doors and windows into these dome structures.
BRIEF SUMMARY OF THE INVENTION
[0012] The present invention overcomes shortfalls in the related
art by disclosing a dome structure that may be efficiently
fabricated with Structural Insulated Panels (SIPs) or other
conventional planar building materials. The invention also presents
a unique connection system wherein each SIP panel is connected by a
spline design using a flexible or living hinge. Unlike Gavette, no
internal support system is needed.
[0013] The invention, sometimes referred to herein as a "geodesic
rhombic triacontahedron" or the proposed "geodesic triacontahedron"
is a space enclosing structure based upon the dual
icosahedron/dodecahedron. The dual of these of these two platonic
solids has two sets of vertices, one set for the icosahedron and
one set for the dodecahedron. The two sets of vertices are located
at different radial lengths from the center of this three
dimensional dual. Further refinements of this dual geometry produce
a rhombic triacontahedron with each diamond-shaped rhombus
subdivided by two diagonals at the midpoint of the rhombus. The
vertices of the original icosahedron and dodecahedron, and the
midpoints of the rhombi, are projected such that all resulting
vertices are of equal radial length from the center of the
triacontahedron. A single sphere circumscribing this geometry would
touch all resulting vertices.
[0014] The resulting spherical geometry can be seen as composed of
a "weave" of great circles, each of which could subdivide the
sphere into two identical hemispheres. The preferred embodiment of
this spherical geometry is a dome or hemisphere with a great circle
as its base and two great circle segments crossing at its apex.
This hemisphere or dome is composed of 60 near right triangles.
These basic triangles are identical in interior angles and side
lengths, with 30being mirror geometries of the other 30.
[0015] The basic geometry of the disclosed design produces
advantageous resolutions to several of the design limitations
inherent in dome architectures based on other geometries. The
present invention has the following advantages over the related
art: 1) Only one basic triangle is utilized to accomplish geodesic
projection, thus reducing manufacturing costs and installation
time; 2) All manifestations of the basic geometry are hemispheric
domes, thus maximizing the efficiency of enclosed space and
building materials; 3) An intersection of two great circle segments
at the geometry's apex allows for attractive and efficient
rectilinear floor plans; 4) The basic triangle closely approximates
a right triangle, thus minimizing costly waste in cutting the
triangles from conventional rectangular stock.
[0016] Unlike prior dome designs, the disclosed geodesic
triacontahedron hemisphere can be divided into even halves, and
further divided into even quarters. The half dome sections can be
separated in one direction and bridged with rectangular elements,
and the quarter dome sections can be separated in two directions
and bridged with rectangular elements. This separation and bridging
creates new geometries that we have termed one direction extension
and two direction extension Geodesic Triacontahedron domes.
[0017] These dome extensions produce several new and advantageous
design features not seen in other dome structures. These design
features are: 1) increased ratio of enclosed space to the surface
area of the dome, 2) increased ratio of enclosed floor area to the
height of the dome, 3) the capacity to increase the dome's enclosed
space and floor area without increasing the size of the basic
triangle, 4) the option for functional segregation of the enclosure
based on the extended portion's more rectilinear and utilitarian
geometry, 5) increased potential for rectilinear floor plan
divisions due to the increased use of great circles segments and
the straight joints of the extension panels, and 6) the capacity
for an extended half dome to be attached as an addition to
conventional rectilinear structures.
[0018] The preferred embodiment of the disclosed design utilizes
Structural Insulated Panels (SIPs) as the material from which the
dome triangles are formed. A SIP is a very strong,
pressure-laminated building material typically consisting of an
outer and an inner face made form an engineered structural board
such as Oriented Strand Board (OSB) and an insulating inner core of
rigid plastic foam. Although SIP stock with other parameters is
manufactured, the preferred embodiment is based on rectangular SIP
stock which is 8 feet wide with a thickness varying from 6.5'' to
12.15'' inches. These dimensions, coupled with the basic triangle's
close approximation to a right triangle, minimize SIP stock waste,
and maximize thermal and building efficiency in most anticipated
applications. However, the disclosed design and its extensions are
not limited to these SIP parameters, or even to SIP utilization in
general.
[0019] Two different cutting patterns are used to generate the
proposed basic triangle in two different sizes. Thus, these two
cutting patterns generate two hemispheric domes of differing
diameters. Due to their thickness, the basic triangles generated
from SIP stock are "beveled" in order to fit together to form the
proposed Geodesic Triacontahedron dome.
[0020] The use of SIPs to implement the proposed Geodesic
Triacontahedron dome and its extensions produces the advantageous
and synergetic interaction of three factors. These factors are: 1)
The strength to weight ratio of the SIP surpasses that of
conventional building materials and ideally matches the parameters
of the proposed domes and their extensions; 2) The beveled edges of
the insulated triangles, along with the relatively few number of
components required to construct the dome, ensure extreme thermal
efficiency; 3) The single installation of a triangular SIP in the
proposed design replaces the "stick-built" tasks of framing,
sheathing and insulating, thus saving a substantial amount of
labor.
[0021] The use of near right triangles makes Structural Insulated
Panels or SIPs an economical alternative to traditional building
materials. The thickness of the SIPs requires that each triangular
panel be beveled in order to fit together to form the geometry of
the invention. Each edge of the triangular panel has a different
dihedral angle of approximately 2, 20, or 30 degrees.
[0022] The three different dihedral angles and the related beveling
necessary to accommodate the various angular interfaces for all
possible pairs of adjacent panels present unique challenges for
panel construction. These challenges are solved by the disclosed
connection system that uses a spline design with a flexible or
living hinge. The splines are extruded in lengths to match the
length of all possible joints between adjacent panel edges.
[0023] A hub system is also disclosed to speed installation time
and to make construction of the dome safer. These designed hubs are
welded steel and all sixty of the dome triangles are connected to
these hubs. The resulting increase in structural integrity makes
the dome panels securely connected to each other and to the ground.
These hubs also are part of the temporary support system during
assembly to support the partial dome until all components are in
place and the dome is self-supporting.
[0024] These and other objects and advantages will be made apparent
when considering the following detailed specification when taken in
conjunction with the drawings. FIGS. 11, 12, 13, 14, 15, 16, 17,
18, 26, and 27 are subject to copyright protection held by Michael
Thompson Morley.
BRIEF DESCRIPTION OF THE DRAWINGS
[0025] FIG. 1 is a perspective view of an Icosahedron solid.
[0026] FIG. 2 is a perspective view of a Dodecahedron solid.
[0027] FIG. 3 is a perspective view of an Icosa/Dodeca dual.
[0028] FIG. 4 is a perspective view of a Rhombic
Triacontahedron.
[0029] FIG. 5 is a perspective view of a Subdivided Rhombic
Triacontahedron.
[0030] FIG. 6 is a perspective view of a Geodesic Rhombi
Triacontahedron with vertices projected in accordance with the
principles of the invention.
[0031] FIG. 7 is a perspective view of a hemisphere in accordance
with the principles of the invention.
[0032] FIG. 8 is a perspective view of the dome in accordance with
the principles of the invention with a stem wall and an extension
bridging the great circle segments.
[0033] FIG. 9 is a perspective view of the dome in accordance with
the principles of the invention with a stem wall and an extension
raising above the great circle segments.
[0034] FIG. 10 is a perspective view of the disclosed geometry.
[0035] FIG. 11 is a perspective view of a Structural Insulated
Panel or SIP
[0036] FIG. 12 is a perspective view of a panel connection
assembly.
[0037] FIG. 13 is an exploded view of a panel connection
assembly.
[0038] FIG. 14 is an exploded view of a hub assembly.
[0039] FIG. 15 to FIG. 18 are plan views of basic triangles used to
construct the dome structures in accordance with the principles of
the invention.
[0040] FIG. 19 is a top view of a hemisphere in accordance with the
principles of the invention.
[0041] FIG. 20 is a front view of a hemisphere in accordance with
the principles of the invention.
[0042] FIG. 21 is a top view of two half domes moved apart with
extension elements added in accordance with the principles of the
invention.
[0043] FIG. 22 is a front view of two half domes moved apart with
extension elements added in accordance with the principles of the
invention.
[0044] FIG. 23 is a top view of four quarter domes moved apart with
extension elements added in accordance with the principles of the
invention.
[0045] FIG. 24 is a front view of four quarter domes moved apart
with extension elements added in accordance with the principles of
the invention.
[0046] FIG. 25 is a plan view of spline design.
[0047] FIG. 26 is a plan view of cutting patterns used on flat
construction material in accordance with the principles of the
invention.
[0048] FIG. 27 is a plan view of splines in place.
DETAILED DESCRIPTION OF THE INVENTION
[0049] The following detailed description is directed to certain
specific embodiments of the invention. However, the invention can
be embodied in a multitude of different ways as defined and covered
by the claims. In this description, reference is made to the
drawings wherein like parts are designated with like numerals
throughout. Unless otherwise noted in this specification or in the
claims, all of the terms used in the specification and the claims
will have the meanings normally ascribed to these terms by workers
in the art.
[0050] The Basic Geometry
[0051] Platonic solids are three-dimensional geometries in which
each face of the particular solid is identical to all the other
faces. In addition, the angles of each face and the length of each
face edge are identical. In other words, each platonic solid is
symmetrical in every way possible. The platonic solids are the:
tetrahedron, octahedron, cube, icosahedron, and dodecahedron.
[0052] Buckminster Fuller used some of the platonic solids as the
basis for his development of the geodesic dome. In the geodesic
dome the faces of a platonic solid are triangulated. Both the
vertices of the original platonic solid and the new ones formed by
the face triangulation are centrally projected to a theoretical
sphere. This imaginary sphere circumscribes the original platonic
solid, touching both the original and new vertices in what can be
termed a geodesic projection.
[0053] The most well-known and utilized of Fuller's geodesic domes
is constructed as described above, using the icosahedron as the
base platonic solid, and geodesic triangulation of each icosahedron
face as the method of practical implementation
[0054] Problems with Conventional Geodesic Domes
[0055] Conventional geodesic domes produced from the icosahedrons
have an attractive appearance, but suffer from several practical
restrictions. Some of these design limitations are discussed
below:
[0056] Complexity of triangulation--Even the simplest geodesic
triangulation of each icosahedron face typically requires two
different triangles, each with its own size and angles. This added
complexity increases construction cost and installation time.
[0057] Hemisphere configuration--Hemispheric domes generally offer
the most efficient use of building materials and enclosed space.
However, before a truly spherical hemispheric dome can be
generated, triangulation of each icosahedron face must become much
more complex, requiring several different triangles.
[0058] Interface with interior walls--Efficient residential floor
plans are generally derived from primarily rectilinear room
divisions. Conventional geodesic domes are constructed from
triangles that join to create non-continuous lines and
non-rectilinear line patterns. Therefore, it is nearly impossible
for such domes to have rectilinear floor plans with interior walls
that interface efficiently and attractively with the undersurface
of the dome's triangulated shell.
[0059] Cutting pattern efficiency--Geodesic projections for
conventional domes create triangles that are all nearly
equilateral. Virtually all building materials used to construct a
conventional dome's component triangles are cut from rectangular
stock. Since equilateral triangles overlay very inefficiently on
rectangles, a conventional dome's component triangles are typically
obtained only by wasteful and costly cutting patterns.
[0060] The disclosed design solves many of the limitations of the
icosahedron-based geodesic dome, and creates new and very
advantageous capacities never seen in any prior space-enclosing
geometry.
[0061] The Rhombic Triacontahedron
[0062] In solid geometry when the structures interpenetrate each
other in symmetrical manner the resulting structure is called a
"dual." An icosahedron/dodecahedron dual FIG. 3 is formed when 1)
each edge of the icosahedron crosses, at right angles, an edge of
the dodecahedron at their respective midpoints, 2) each vertex of
the icosahedron is centered above the planar surface of one of the
dodecahedron's faces, and 3) each vertex of the dodecahedron is
centered above the planar surface of one of the icosahedron's
faces.
[0063] Two spheres can be circumscribed around the
icosahedron/dodecahedron dual, one touching the original
icosahedron's vertices, and one touching the original
dodecahedron's vertices. Each sphere has a different radius from
the center of the three-dimensional dual icosahedron/dodecahedron
geometry.
[0064] The right angle intersection of each icosahedron edge with a
dodecahedron edge defines a diamond-shaped plane called a rhombus
FIGS. 3-5, 1. These diamond-shaped rhombic planes form a three
dimensional structure called a rhombic triacontahedron FIG. 4. This
is the original icosahedron/dodecahedron dual with each vertex of
the dodecahedron connecting to three adjacent vertices of the
icosahedron. A sphere that would touch the mid-point of each
rhombic plane, where an icosahedron edge and a dodecahedron edge
intersect, would not circumscribe but would actually be located
inside the rhombic triacontahedron. This sphere would have a radius
from the center of the rhombic triacontahedron that is different
from the radii of either of the first two spheres described
above.
[0065] The Invention, the Geodesic Triacontahedron
[0066] In the description above, we have defined three sets of
vertices for the proposed geometry. Set 1 consists of the vertices
of the original icosahedron FIG. 10, 2. Set 2 consists of the
vertices of the original dodecahedron FIG. 10, 3 and, Set 3
consists of the midpoints of the rhombic planes FIG. 10, 4 of the
derived rhombic triacontahedron. Each of these three sets is at a
different radial distance from the center of the dual
icosahedron/dodecahedron (now a rhombic triacontahedron). In the
proposed geodesic geometry, FIG. 6, the radial distance from the
center of the three dimensional rhombic triacontahedron is made
consistent for all three sets, so that a single circumscribed
sphere touches all resulting vertices in all three of these sets.
This proposed geometry has 62 vertices, 120 triangular faces and
180 edges. It is an efficient approximation of the circumscribed
sphere, as all 120 triangles have the same angles and size, with 60
triangles being mirror images of the other 60. We have chosen to
call this figure a Geodesic Triacontahedron.
[0067] The primary elements of the proposed design are the
parameters for the basic triangle FIG. 10, 5 that forms this
geodesic geometry. FIG. 26 is a plan view of two sizes of the basic
triangle as cut from Structural Insulated Panels (SIPs), or other
similar rectilinear stock. FIGS. 15, 16, 17 and 18 depict the
angles and dimensions of these two size variations of the basic
triangle.
[0068] A key characteristic of the proposed geometry is that the
edges of contiguous triangles form only great circles. A great
circle is a continuous straight line extending across the surface
of a sphere which, like the equator of the earth, cuts the sphere
into two equal hemispheres. Thus, the original geometric
triacontahedron divides evenly into two equal hemispheres along any
of this geometry's great circles. This is a characteristic that
most of the less complex icosahedron-based geodesic domes do not
have. As hemispheric domes typically represent the most efficient
use of materials and interior space, this is an important
functional consideration.
[0069] Once a hemisphere is created from the original
triacontahedron sphere and positioned with its "equator" on the
ground or a flat base, the top view of this structure reveals
segments of two of the original great circles intersecting at right
angles at the hemisphere's apex FIG. 19, 6 where 7-8 and 9-10 show
two great circles interesting at point 6. These great circle
segments have the functional properties of complete great circles
and, for simplicity, are referred to herein as "great circles". The
intersection of these two great circles gives the proposed design
certain advantages over conventional domes, as described below.
This great circle intersection also serves as the basis for
"extensions" of the basic proposed geometry, as further described
below.
[0070] Advantages of the Invention
[0071] As stated before, conventional geodesic domes constructed
from icosahedron-based geometry suffer from several design
restrictions. The basic geometry of the proposed design resolves
these design limitations, as described below:
[0072] Complexity of triangulation--As opposed to the conventional
geodesic dome, the proposed design accomplishes geodesic projection
with only one basic triangle. No matter what its size, the basic
geometry of the proposed design is comprised of only sixty of these
triangles (30 being mirror images of the other 30). This design
simplicity reduces construction costs and installation time.
[0073] Hemisphere configuration--As opposed to conventional
geodesic domes, all manifestations of the basic geometry are
hemispheres, which typically offer more efficient use of building
materials and space than any other dome configuration.
[0074] Interface with interior walls--As opposed to the "broken"
and non-rectilinear joint patterns of conventional geodesic domes,
two straight great circles intersect at right angles at the apex of
the Geodesic Triacontahedron dome. Interior walls can be "dropped"
from the undersurface of the dome's shell anywhere along each
straight and continuous great circle. Such walls interface
attractively and efficiently with the dome's undersurface. In
addition, because interior walls can follow both of the great
circles intersecting at 90 degrees, a large variety of
predominately rectilinear floor plans can be generated.
[0075] Cutting pattern efficiency--As opposed to the conventional
geodesic dome's nearly equilateral component triangles, the basic
triangle used to accomplish geodesic projection for the proposed
design closely approximates a right triangle, distorted only
slightly from 90 degrees for the spherical application. Since right
triangles overlay rectangular building material stock very
efficiently, cutting patterns that minimize waste and cost are
obvious. FIG. 26 shows examples of such efficient cutting
patterns.
[0076] Dome Extensions
[0077] The proposed Geodesic Triacontahedron dome with two great
circles intersecting at right angles at the hemisphere's apex is
depicted in FIG. 19, 6. The hemisphere can be subdivided into two
"half domes" along either of these great circles. These half domes
can then be moved apart and rectangular structural elements
inserted to bridge the space between the triangles on each half
dome that were adjacent before this separation. This can be thought
of as a single extension of the Geodesic Triacontahedron dome, as
the dome is extended in a single direction FIG. 21 and FIG. 22.
[0078] Dividing the original hemispheric dome into four-quarter
domes along intersecting great circle creates the second variation
of the Geodesic Triacontahedron dome. The four-quarter domes are
moved apart in two directions and rectangular structural elements
are inserted to bridge the space between the triangles on each
quarter dome that were adjacent before this separation. This can be
thought of as a double extension of the Geodesic Triacontahedron
dome, as the dome is extended in two directions FIG. 23 and FIG.
24.
[0079] Advantages of Dome Extensions as used with the Invention
[0080] Some of the more complex icosahedron-based geodesic domes
can be constructed as hemispheres. But none of these
icosahedron-based domes can be "halved" or "quartered" in the way
that the Geodesic Triacontahedron dome can be sectioned and
extended. The extension variations of the basic Geodesic
Triacontahedron dome give it distinct advantages over the
conventional geodesic dome. Some of these advantages are:
[0081] Increased space enclosure--The "stretched" portion of the
extended Geodesic Triacontahedron dome can be considered vaulting.
Such vaulting encloses more space per unit of external surface area
than the triangulated or domed portion of the structure. Thus, the
overall space enclosed per unit of external surface area is
increased. The rectangular structural elements are less costly to
produce than the triangular elements. Thus, the cost per unit of
enclosed space is reduced.
[0082] Increased space utility--The typical way to increase useable
floor area in a conventional icosahedron-based geodesic dome is to
increase the diameter of the dome. However, this automatically
increases the dome's height. This height increase encloses more
vertical space, which often cannot be utilized efficiently on the
first floor and does not add sufficient height to permit a second
floor. The end result is more construction costs and more unused
space to heat/cool. The Geodesic Triacontahedron dome can be
extended in increments to increase first floor area without
increasing the overall height of the dome.
[0083] Consistent size of dome triangles--As discussed above,
conventional icosahedron-based geodesic domes are increased in
diameter to enclose more floor space. When this occurs, the
triangular components of the dome must either increase in size, or
the number and variety of triangular components must increase. In
either case this can increase construction and installation costs.
On the other hand, the Geodesic Triacontahedron dome's triangular
components are all composed from the same shape (or its mirror
image). When this dome is extended as described above, its floor
space increases, but the size of its triangular components remains
the same. This has important implications for manufacturing and
installation as further described herein.
[0084] Optional segregation of function--A dome's shell is
typically constructed from flat triangles that are joined at
angles. From inside the dome, the dome's shell can be seen as
angling in two directions--left/right and up/down. This two-way
curvature is the reason that domes do not easily conform to
rectilinear standards for exterior doors, windows, furniture,
cabinetry, countertops, home appliances, etc. However, the Geodesic
Triacontahedron's vaulted dome extensions curve in only one
direction--up/down. Thus, the single-curve of dome extensions is
much more "rectilinear friendly" than the dual-curving dome
shell.
[0085] This distinction promotes a natural segregation of function,
with the more work-oriented areas located under the vaulted dome
extensions, and the more leisure-oriented areas located under the
dome shell. Following this functional segregation, many rectilinear
building and furnishing components, such as exterior doors,
countertops and large appliances, would be located in the vaulted
extension.
[0086] The proposed Geodesic Triacontahedron dome and its optional
extensions are designed to create a highly efficient
space-enclosing structure. Many possible applications will be found
for these structures, with most of these uses revolving around
human-oriented living and/or working space. Such uses may include
home construction, churches, grade schools, small industrial
buildings, temporary disaster housing, and remote research station
construction.
[0087] The optional segregation of function that dome extensions
provide might be applied to a large number of these possible
applications. For example, in a single extension Geodesic
Triacontahedron home the living and dining areas might be located
in one dome end with the master bedroom and bath located in the
other dome end. The kitchen, laundry area, children's bedrooms and
baths would be located in the middle, vaulted extension section. A
larger extended dome might used as a small grade school with
classrooms located in the middle vaulted area, and the two half
domes enclosing a gym/auditorium at one end and a cafeteria at the
other. When used as a research station, the extended dome's vaulted
section might enclose the research area, with a dormitory under one
half dome and a common eating/social area under the other half
dome.
[0088] Interface with interior walls--As noted earlier, the shells
of most conventional domes lack great circles. Consequently, these
structures typically lack a clean interface between the
undersurface of the dome's triangulated shell and the dome's
interior walls. The basic geometry of the proposed Geodesic
Triacontahedron dome resolves this design problem by "dropping"
straight interior walls or wall sections from the dome shell's
great circles. If all of the space below these two great circles
were to be utilized as interior walls, the dome could be seen as
having two long straight walls, with each wall completely bisecting
the dome's base and each wall intersecting the other wall at 90
degrees, FIG. 19, lines 7-8 & 9-10.
[0089] A single extension of the basic geometry increases the
length of the top of one the great circles by exactly the length of
the extension itself FIG. 21, line 11-12. At 90 degrees to this
lengthened great circle, a third great circle is formed FIG. 21,
line 13-14. Additional interior walls can be dropped from both the
great circle extension and the third great circle. Furthermore, two
of the seams connecting the rectangular extension panels are high
enough on the dome to allow interior walls to be dropped from them
FIG. 21, line 15-16 & 17-18.
[0090] A double extension of the basic geometry creates four great
circles, each one lengthened by the length of the extension.
Interior walls can be dropped from these extended great circles, as
well as from the four extension panels seams just below the
intersections of the four great circles FIG. 23 and FIG. 24.
[0091] Well-designed floor plans might not utilize every
opportunity for interior walls provided by great circles, great
circle extensions and extension panel seams. However, the
descriptions above illustrate that the proposed dome extensions
promote clean and efficient interfaces between the dome shell and
the dome's interior walls. Thus, these dome extensions
significantly increase the degree to which rectilinear floor plans,
and other rectilinear conventions, can be utilized with the
proposed design.
[0092] Interface with conventional construction--The conventional
icosahedron-based geodesic dome cannot be evenly sectioned to serve
as an attachment or addition to conventional rectilinear buildings.
As described above, the disclosed design can be "halved" evenly. A
half dome (one quarter of the whole geometric sphere) can be easily
attached to a conventional structure which has a vertical wall
height higher than the apex of the half dome. Dome extensions often
increase the size and/or functionality of such an addition. For
example, a single extension, as described above, could attach a
half dome to the rear of a conventional home to create an elegant
master bedroom suite.
[0093] The preferred geometric embodiment of the disclosed design
is described in detail in the preceding sections. In summary, this
geometric embodiment comprises a subdivided rhombic triacontahedron
with the vertices of its component icosahedron and dodecahedron,
and the midpoints of its component rhombi, projected to all touch a
theoretical circumscribed sphere. This can be termed a geodesic
geometric solution. The hemispheric dome derived from this basic
geometry has many practical advantages that are derived from 1) its
inherent great circle segments, and 2) its near right angle basic
component triangles. It is to be noted that non-geodesic
approximations of this basic geometry might be created that would
also form great circle segments and near right angle basic
component triangles. In such non-geodesic geometric solutions all
the vertices might not touch a circumscribed sphere. These
non-geodesic solutions are included in this general design as
non-preferred geometric embodiments.
[0094] The Preferred Construction Embodiment--Structural Insulated
Panels ("SIPs")
[0095] The proposed Geodesic Triacontahedron dome and its
extensions are designed as space-enclosing structures which can be
constructed from a variety of building materials using several
building techniques. Many of the materials and techniques used to
construct conventional icosahedron-based geodesic domes might also
be used to construct the proposed design. Such materials might
include plywood or pressboard exteriors and drywall interiors.
Building techniques might include prefabrication of the triangular
and rectangular components or fabrication "on-site." The components
might fit together directly using a variety of connectors. Or, a
"hub-and-strut" shell might be constructed using metal hubs and
wood struts. The triangular and rectangular components could then
be attached to this geometric framework.
[0096] Though the disclosed design can utilize many of these
alternatives, there is one building material that is seen as the
most efficient and elegant match for the proposed geometries. This
material is the Structural Insulated Panel (SIP). The following
description outlines a preferred embodiment of the disclosed design
using Structural Insulated Panels. However, description of this
preferred embodiment should not be viewed as limiting the overall
potential of the disclosed design to be utilized with other
building materials and building techniques.
[0097] A SIP comprises of two outer skins and an inner core of an
insulating material which has been pressure-laminated together.
When properly bonded, these three components act synergistically to
form a composite that is much stronger than the sum of its parts.
The outer skins typically consist of Oriented Strand Board, though
plywood or other materials are sometimes used. The core of SIPs can
be made from a number of materials including molded expanded
polystyrene, extruded polystyrene and urethane foam. Stock SIPs are
produced in thicknesses from 4.5 inches to 12.25 inches and in
sizes from 4 feet by 8 feet up to 9 feet by 30 feet.
[0098] Advantages of SIP Embodiment
[0099] The SIP is envisioned as the preferred embodiment for the
proposed Geodesic Triacontahedron dome because of the strength,
thermal efficiency and labor-saving economy that this building
material will bring to the implementation of the disclosed design.
These three factors are discussed below:
[0100] SIP strength--Structural Insulated Panels meet the
structural requirements of all the major building codes. The axial,
transverse and racking load capabilities of these panels will give
this dome strength to weight ratios unavailable with conventional
building methods. All of the spans generated by each size
configuration of the dome triangles are well within the structural
limits of the panels, and, like an "I" beam, the strength of the
SIP panel increases as its cross-sectional depth or thickness
increases. Therefore, under extreme weather conditions or special
architectural requirements, a thicker cross section would be
specified. This capacity for SIP strength to be increased makes it
a perfect match for the design flexibility of the proposed dome
design and its extensions.
[0101] SIP thermal efficiency--The insulating cores of the panels
offer very high R-values per inch of material, and the small number
of pieces required to complete the structure results in fewer seams
and a much tighter structure compared to conventional buildings. In
addition, the method of finishing and joining the triangles' edges,
as described below, creates a structure with no thermal bridging
except next to doors and windows.
[0102] SIP labor-saving economy--The installation of a three-layer
laminated SIP takes the place of three separate "stick-built"
operations. In a single installation procedure the tasks of
framing, sheathing and insulating are eliminated, thus saving a
substantial amount of labor. The inherent labor-saving economy of
SIP installation is substantially increased with the proposed
design, given the fact that only 60 triangles are assembled. This
is compared to many hundreds of pieces required to frame a
conventional geodesic dome or a conventional "stick-built"
home.
[0103] SIP Cutting Patterns
[0104] The SIP is presented in this disclosure as the preferred
embodiment of the disclosed design. This should not be viewed as
limiting the disclosed design to being constructed with SIPs. In
addition, an extremely efficient utilization of the SIP is
presented below as the preferred embodiment of the SIP-based
Geodesic Triacontahedron dome. This should not be viewed as
limiting the disclosed design to the cutting patterns, the cut SIP
size, or the dome diameters described below. Rather, these
descriptions should be seen as illustrating the efficiency and
synergetic potential of using SIPs to construct the disclosed
design.
[0105] Over the last few years the SIP industry has evolved to the
point where certain standards are well-established. One of these is
the standard size of the SIPs. Almost all SIP manufacturers produce
SIPs with a minimum width of 8 feet, and a maximum size of 9 feet
.times.30 feet. Though SIPs wider than 8 feet do exist, 8 feet is
most common SIP width and is used as a standard in these
calculations. However, the disclosed design should not be
considered to be limited to 8 foot wide SIP material.
[0106] The width of the panels is the key factor in orienting the
basic triangle on rectangular SIP stock to produce various cutting
patterns. Orienting the basic triangle's hypotenuse along the 8
foot SIP width produces a very inefficient cutting pattern and a
very small dome diameter. This alternative will not be considered.
However, orienting either of the triangle's shorter sides along the
8 foot SIP width produces extremely efficient cutting patterns.
This is due to the fact that either of these orientations takes
advantage of the triangle's near right angle. These orientations
allow cutting patterns that are, in essence, a series of
near-rectangular parallelograms that minimize SIP cutting waste,
FIG. 26. 19 of FIG. 26 shows the minimal areas of waste, while 20
shows optional panel truncation to allow for skylights and greater
panel size.
[0107] By alternately orienting each of the triangle's two short
sides along the 8 foot SIP width, two basic cutting patterns are
generated. Each basic pattern produces a different-sized triangular
component, which in turn produces a dome with a particular diameter
and enclosed square footage.
[0108] Panel Connections
[0109] The thickness of the SIP, as described above, requires that
each triangular panel be "beveled" in order to fit together to form
a structurally-sound Geodesic Triacontahedron dome. Each edge of
the triangular panel will have a different dihedral angle.
[0110] Making such precise beveled cuts in SIP panels has been made
possible only very recently by the development of expensive
computerized European saws installed in the last three years in a
handful of American SIP manufacturing plants. This technology is
literally at the cutting edge of the SIP industry and enables the
manufacture of the proposed triangular panel as an extremely
efficient, low-cost building material.
[0111] Given the necessary triangular shape and beveled edges of
the proposed SIP panels, connecting these panels presents unique
challenges. The invention's connecting design utilizes a "spline"
design based on a formula composite manufactured from extruded PVC
or a foamed polypropylene. The splines are extruded in lengths to
match the length of all possible joints between adjacent panel
edges.
[0112] The structural connections between triangles are made when a
spline is inserted into slots in the foam under the exterior and
interior skins of adjacent SIP panels, FIG. 27, 21. These slots,
which are pre-cut during the manufacturing process, are made
slightly larger than the splines for ease of installation. After
installation, the splines are pulled into their final position with
screws, drilled through the exterior of the skins and screwed into
the splines, pulling the splines tight up against the inside of the
skin FIG. 27, 22.
[0113] Three different angles (approximately 2 degrees, 20 degrees,
and 30 degrees) are used to accommodate the various angular
interfaces for all possible pairs of adjacent panels, FIG. 27.
Ideally one spline design could be utilized to connect all possible
pairs of adjacent panels despite their differing angular
interfaces. FIG. 25A, 25B, and 25C show two possible methods of
extruding the splines with a living hinge. In these methods the
splines are extruded as a composite incorporating reinforcing
threads or pieces. In the first method, FIG. 25A the splines are
extruded with a living hinge created by the extrusion process. In
this method, the reinforcing material is evenly distributed
throughout the spline.
[0114] In the second method, FIG. 25B the spline is extruded
without a living hinge. The living hinge is created as a second
step when the previously extruded spline is compressed or stamped,
FIG. 25C. This method has the possible advantage of having
relatively more reinforcing material concentrated in the area of
the living hinge where added strength may be useful. In contrast,
the wider portions of the spline have relatively less reinforcing
material. This may allow the screws drilled through the skins of
the SIPs to more easily penetrate the wider portions of the
splines.
[0115] While this panel connection system is designed to connect
the basic components of the proposed Geodesic Triacontahedron
design, it has wider applications. The disclosed panel connection
system could be used in many construction situations where two SIPs
need to be attached to each other at angles less than approximately
180 degrees but greater than approximately 90 degrees.
[0116] Foundation Connections
[0117] The base course of SIP panels is connected to the foundation
by attaching the bottom of the first course panels to the
foundation or floor deck. To accommodate the base plate, the edge
foam is relieved from the bottom face of the base panel to the
depth of the base plate. When panels are installed on concrete or
on other material not compatible with wood, a base plate assembly
is bolted to the foundation by code approved connection methods and
the SIP triangle is connected to the plate with screws attached
horizontally.
[0118] Hubs and Jigs
[0119] As noted previously, the eight-foot width of the standard
manufactured rectangular SIP panel sets the parameters for very
efficient triangular panel cutting patterns. However, by truncating
the acute ends of these triangles, larger panels can be cut from
the same standard rectangular SIP FIG. 26, 20. FIG. 11 shows an
8.times.24 foot SIP cut into the disclosed near right triangles and
used to construct the disclosed structure. The space created by the
truncating of the triangles leaves room for a structural hub that
greatly strengthens the dome. The hubs are also used to help
stabilize the dome during assembly before the dome becomes stable
when all pieces are in place. The designed assembly jig aligns,
supports and stabilizes the structure.
[0120] FIG. 12 shows panel connection details. FIG. 13 and FIG. 14
show hub and spline details.
* * * * *