U.S. patent number 3,662,486 [Application Number 05/008,510] was granted by the patent office on 1972-05-16 for polyhedral amusement and educational device.
Invention is credited to Edward J. Freedman.
United States Patent |
3,662,486 |
Freedman |
May 16, 1972 |
POLYHEDRAL AMUSEMENT AND EDUCATIONAL DEVICE
Abstract
A series of polyhedrons are removably and rotatably connected to
each other to form a series. Each polyhedron has an edge which lies
in a plane perpendicular to a plane containing either an opposite
edge, as in the case of a tetrahedron, of a point, as in the case
of a trihedron. The opposite edges, or edge and opposite point are
adapted to contain hinge elements which may be removably and
rotatably connected. When in the form of a closed loop, containing
at least four connected polyhedrons, the device is capable of being
continuously turned up to 360.degree. inside itself to form a
multitude of geometrical shapes and configurations. For any given
closed loop, the geometric form of the configurations is dependent
upon the number and type of polyhedrons employed.
Inventors: |
Freedman; Edward J. (Glencoe,
IL) |
Family
ID: |
21732008 |
Appl.
No.: |
05/008,510 |
Filed: |
February 4, 1970 |
Current U.S.
Class: |
446/120;
52/DIG.10; 273/155; 428/542.2; 220/DIG.13; 434/403 |
Current CPC
Class: |
A63H
33/065 (20130101); A63F 9/088 (20130101); Y10S
52/10 (20130101); Y10S 220/13 (20130101) |
Current International
Class: |
A63F
9/06 (20060101); A63F 9/08 (20060101); A63H
33/04 (20060101); A63H 33/06 (20060101); A63h
033/00 () |
Field of
Search: |
;46/1,23,24,24,26,30,31
;35/72 ;273/155 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Peshock; Robert
Claims
I claim as my invention:
1. An instructional and amusement device which comprises a series
of congruent triangular tetrahedrons, the opposite edges of which
are formed from equal dihedral angles, equipped at a pair of said
opposite edges with hinge element means whereby said tetrahedrons
may be removably and rotatably connected to form said series.
2. The device of claim 1 further characterized in that at least six
of said congruent triangular tetrahedrons are connected to form a
closed loop.
3. A device of claim 1 further characterized in that the angles of
the triangular faces of said tetrahedrons are acute.
4. The device of claim 1 further characterized in that the four
faces of said tetrahedrons are congruent isosceles triangles.
5. The device of claim 1 further characterized in that two opposite
faces of said tetrahedrons are 90.degree. triangles.
6. The device of claim 5 further characterized in that said faces
are 30.degree.-60.degree.-90.degree. triangles.
Description
APPLICABILITY OF INVENTION
The present invention primarily involves a series, or multitude of
building blocks having the shape of polyhedrons. As hereinafter set
forth in greater detail, the polyhedrons are equipped with
connecting means, for example, hinge elements, such that individual
polyhedrons may be connected to each other to form an elongated
string or series. These polyhedrons may take the form of trihedrons
or tetrahedrons; preferably, an individual string or series of
polyhedrons constitutes either all tetrahedrons, or all trihedrons.
Four or more polyhedrons can be joined to form a closed loop which
is capable of being turned up to 360.degree. inside itself.
The device which is encompassed by my invention, whether in the
form of a closed loop, or as an elongated string or series, is
simultaneously an amusement and entertaining toy, and an
educational, or instructional device. Obviously, the device of this
invention is designed to be used by and for children in the general
age range of from 2 to about 12 years. However, it is understood
that the same can well be a form of amusement for those older than
12 years--adults may well find some degree of amusement and/or
therapeutic benefit therefrom. With respect to the relatively young
child, to whom the present invention is specifically directed, the
device encompassed by my invention can aid and assist in attaining
motor coordination, dexterity, and a sense of physical and mental
balance. Further, the child will increase his perception respecting
symmetry, and further develop his sense of differentiation in
spatial and/or geometrical relationships. The interchangeability of
the device, especially when in the form of a closed loop, which, as
hereinbefore set forth, produces a variety of geometrical
configurations, can be utilized as a type of psychological testing
device. In a manner similar to the well-known Rorschach Ink-Blots,
the present device can be of value with respect to young children
recognizing and stressing either the background, or the foreground
of a given geometrical form having one particular defined shape as
the background, and another different shape as the foreground.
Additionally, by utilizing any number of polyhedrons, either as a
string, or in a closed loop, the child can "create" his own
sculpture, shape, configuration, or geometrical form.
OBJECTS AND EMBODIMENTS
One object of the present invention is to provide an amusement, or
entertaining toy. A corollary objective affords an educational, or
instructional device.
Another object involves the formation of a series of polyhedrons
which is capable of assuming a multitude of geometric
configurations. Still another object resides in a closed loop of
interconnected polyhedrons, which loop is capable of revolving
360.degree. inside and out of itself.
Other objects and embodiments involve the type of polyhedron
employed, the number thereof in forming the closed loop and the
means by which the polyhedrons are connected to each other. These,
as well as additional objects and embodiments will become evident
from the following more detailed description of my invention.
SUMMARY OF THE INVENTION
As hereinbefore set forth, the present invention is principally
directed toward a polyhedral device which functions (1) as an
amusement or entertaining toy, and (2) as an instructional or
educational aid. Individual polyhedrons are removably and rotatably
connected to each other to form a series, or string which can be
transformed into a multitude of different shapes and/or
configurations, can be folded onto itself at a variety of angles,
formed into abstract sculptures and, when consisting of at least
four polyhedrons, capable of forming a closed loop. Such a closed
loop can revolve up to and including 360.degree. inside itself, and
thereby present a variety of geometrical configurations. These
configurations take the form of a background shape and a different
foreground shape, the precise configurations depending upon the
type and number--i.e., 4, 6, 8, 10, 12, 14, etc.--of polyhedrons
employed. Although not an essential requirement, a preferred series
or closed loop consists of identically shaped polyhedrons.
Probably the most common and well-known polyhedron is a regular
tetrahedron, otherwise termed a "pyramid." While the tetrahedral
shape is a preferred form of the "building block," trihedrons can
also be connected and formed into a series. As will be recognized,
the sides (faces) of the trihedron are curvilinear. The triangular
faces of the trihedron may be 90.degree. triangles, obtuse
triangles, or acute triangles, with the 90.degree. triangle being
preferred.
With respect to the tetrahedral string, or series, regular
tetrahedrons, or pyramids may be employed, in which case all the
faces are, of course, equilateral triangles. Likewise, the
tetrahedron may be formed such that all triangular faces are
congruent, isosceles triangles; two opposite faces are isosceles,
while the other two opposite faces are congruent, acute triangles;
two faces are isosceles, while two are congruent 90.degree.
triangles, for example, 30.degree.-60.degree.-90.degree. triangles;
or, two faces are isoceles, while the other two opposite faces are
congruent, obtuse triangles. A particularly interesting and
intriguing device results from the use of (1) tetrahedrons having
all congruent, isosceles faces, or (2) tetrahedrons having two
congruent 30.degree.-60.degree.-90.degree. faces and two opposite
isosceles faces. Immediately recognized is the fact that the
polyhedrons have an edge which lies in a plane perpendicular to a
plane containing an opposite edge (tetrahedron), or point
(trihedron). In the case of the tetrahedrons, it is preferred that
said opposite edges be of the same length. It is understood that
this preference does not allude to an essential feature of my
invention. Although not as suitable from the standpoint of the
geometrical configurations which evolve, a series could be
constructed--i.e., from 30.degree.-60.degree.-90.degree.
tetrahedrons--where one edge is 1 inch in length (the 90.degree.
edge) and the opposite edge (the edge common to the isosceles
triangular faces) is 11/2 inches long.
With respect to tetrahedrons having four congruent, isosceles
triangular faces, a string or series of four will not form a closed
loop. Six, or any even number more will close to form a loop which
can revolve inside and out of itself 360.degree.. Where the series
is formed from tetrahedrons having two opposite congruent
30.degree.-60.degree.-90.degree. triangular faces, the other two
faces being non-congruent, isosceles triangles, four will not close
to form a loop, but six or more will, and the loop is capable of
the 360.degree. inside/out revolution.
A string of equilateral tetrahedrons (true pyramids) requires six
to close into a loop. The resulting loop can, however be turned
only about 45.degree., or one-half a phase, the latter being herein
considered to be 90.degree.. Eight such connected pyramids will
form the closed loop capable of continuously revolving through the
360.degree. cycle, or four 90.degree. phases.
A strange anomaly is presented when the string is constructed of
tetrahedrons having two opposite faces in the form of congruent,
obtuse triangles. Four, six, eight, or 10 will all close to form a
loop. Only the loop of 10, or more, can successfully complete the
360.degree. cycle. A series of four can revolve 90.degree.,
stopping short of 180.degree.; six will go through 180.degree., but
stops short of 270.degree.; whereas, eight obtuse tetrahedrons will
close and stop short of a complete 360.degree. cycle.
Although the polyhedral "blocks" may be opaque and/or of a single
color, additional advantages and further utility are realized when
the polyhedrons are (1) all transparent, or (2) the various faces
are multi-colored. In the case of transparent polyhedrons, the
otherwise "hidden" edges can be seen, with the result that the
variety of geometric configurations are seen from a different
viewpoint. To emphasize this, the edges can be colored, the
remainder being transparent, such that the edges conspicuously
stand-out. The three-dimensional effect is therefore, accentuated.
Multi-colored polyhedrons, where all faces are differentially
colored, or one or more are identically colored, produce shapes
which are readily distinguishable from each other, and the child
can be easily introduced into the realm of color differentiation.
For example, a form of "puzzle" could be presented where the child
is asked to form a geometrical shape consisting of a "red" octagon
containing a "green" four-pointed star. Another type of puzzle
stems from the fact that, as hereinbefore set forth, a closed loop
comprising all pyramids requires eight to form a closed loop
capable of revolving the complete 360.degree. cycle. If presented
with this problem, the child would soon learn that six segments
will result in a closed loop, but the loop cannot be revolved
360.degree. inside itself.
The individual tetrahedrons, or trihedrons, may be constructed of
any rigid, or semi-rigid material including paper, cardboard, wood
veneer, plastic, etc. The most commercially advantageous scheme
would be to employ injection-molded plastic which has obvious
economical benefit, not to mention the resulting rigid
construction. Other materials are principally suitable for use in
kit form where each polyhedron must first be constructed.
The concept, upon which the present invention is founded, will be
more clearly defined and understood upon reference to the several
accompanying drawings which are directed to one of the principal
embodiments. In the interest of brevity, the drawings are, for the
most part, directed toward a closed loop consisting of eight
30.degree.-60.degree.-90.degree. tetrahedrons. Since these drawings
are presented for illustrative purposes only, and are not intended
to be limiting upon my invention, it will be appreciated that they
are only partially indicative of the multitude of shapes and
configurations which result when the loop is revolved about itself.
As previously stated, the loop can revolve 360.degree., there being
four primary 90.degree. phases. It must be stated, however, that,
during any given 90.degree. "turn," the closed loop assumes an
infinite number of shapes, the precise character of any shape being
dependent upon the particular instant when the revolution of the
closed loop is halted.
DESCRIPTION OF DRAWINGS
With reference now to the accompanying drawings, which are not
necessarily drawn to scale, there is presented an illustration
directed primarily toward a closed loop consisting of identical
30.degree.-60.degree.-90.degree. tetrahedrons.
FIG. 1 is a perspective view of two separated
30.degree.-60.degree.-90.degree. tetrahedrons which can be
connected to each other to initiate the series.
FIG. 2 is a perspective view of three separated trihedral
segments.
FIG. 3 is a plan view of a closed loop, constructed from eight
30.degree.-60.degree.-90.degree. tetrahedrons, as it appears to the
viewer in one stage of the 360.degree. revolution, or cycle.
FIG. 4 is a right-side view of the configuration shown in FIG.
3.
FIG. 5 is a plan view of the shape resulting when that of FIG. 3 is
"squeezed" and rotated left about 45.degree. to bring hinge 20 to
the top.
FIG. 6 is a plan view of the shape which results when the
configuration of FIG. 3 is turned outwardly on itself 90.degree.,
and rotated slightly right to bring hinge 26 to the top.
FIG. 7 is the end view taken along the line 7--7 of FIG. 6.
FIG. 8 is a plan view of the shape resulting when the configuration
of FIG. 6 is turned outwardly on itself another 90.degree..
FIG. 9 is a plan view of the configuration produced when that of
FIG. 8 is "squeezed."
FIG. 10 is a plan view of the shape resulting when the
configuration of FIG. 9 is closed on hinges 23, 25, 27, and 21.
With reference now the individual FIGURES for a more detailed
description, FIG. 1 shows two identical
30.degree.-60.degree.-90.degree. tetrahedrons, 9 and 10, in
perspective. Tetrahedron 9 is equipped on the 90.degree. edge, AB,
with the female half 1 of the hinge element. The opposite edge, DC,
which lies in a plane BCD perpendicular to the plane ABC, is
adapted to contain a male half of a hinge element 4. Similarly,
tetrahedron 10 is equipped with a corresponding male half of a
hinge element 2 on its 90.degree. edge, EF, and a male half of a
hinge element 3 on its opposite edge, GH. The tetrahedrons are
joined by mating hinge elements 1 and 2. Other tetrahedrons are
attached at hinge elements 3 and 4, form a string or series. For
example, a tetrahedron identical to 9, having a male half of a
hinge element 4, is connected to tetrahedron 10 at the edge GH.
Although not essential, as hereinbefore stated, the edges DC, AB,
EF, and GH are identical in length. This aspect provides a more
practical and eye-pleasing device as hereinafter indicated. It
should also be noted that one tetrahedron, 9 has the female half of
the hinge element on its 90.degree. edge, while the other
tetrahedron 10 has the male half on its 90.degree. edge.
FIG. 2 presents three 90.degree. trihedrons, 11, 12, and 13, and
indicates that the "triangular" faces, 14, 15, 16, 17, 18, and 19,
are curvilinear. With respect to trihedron 11, the 90.degree. edge
KL, contains a male half of a hinge element 6, while trihedron 13
is adapted with a female hinge element 7 at its 90.degree. edge,
MN. It should be noted that both points J and O lie in planes which
are perpendicular to the planes containing 90.degree. edges KL and
MN, respectively. Points J and O are adapted to contain female
hinge element 5 and male hinge element 8, respectively. Trihedron
12 is identical to trihedron 11, having a female hinge element 5'
at point P, and a male hinge element 6' at the 90.degree. edge QR.
It will be readily ascertained that the joint formed by hinge
elements 8 and 5' rotates on a 90.degree. axis with respect to the
joint formed by mating hinge elements 6 and 7.
In FIG. 1, hinge element halves 1 and 2, and 3 and 4 are in the
form of modified common door hinges. Rather than employ a hinge
pin, which is suitable, but too small for the very young child, the
hinge elements are preferably constructed either in a manner such
that they may be readily snapped together, or as a slip-on type.
The latter is shown in FIG. 2 wherein hinge element 8 may be
connected to hinge element 5' by simply sliding the former into the
latter. The slip-on type hinge may also be used the full length of
the 90.degree. edges in FIG. 1 and on the 90.degree. edges of the
trihedrons in FIG. 2. Other connecting means are well within the
purview of those skilled in the art, and it is understood that the
use of a specific connecting means is not an essential feature of
my invention.
FIG. 3 is a plan view of a closed loop, constructed from eight
30.degree.-60.degree.-90.degree. tetrahedrons, as it appears to the
viewer at one stage, or phase of a complete 360.degree. revolution,
or cycle. The loop is formed by alternately connecting four each of
tetrahedrons 9 and 10 by way of hinges 20, 21, 22, 23, 24, 25, 26,
and 27. Eight congruent, isosceles triangular faces, 28, 29, 30,
31, 32, 33, 34, and 35, shaded for the purpose of contrast and a
more clear illustration, are seen to form a four-pointed star, as
the foreground configuration, within a perfect square, as the
background configuration. The eight
30.degree.-60.degree.-90.degree. triangular faces 44, 45, 46, 47,
48, 49, 50, and 51, are seen to the viewer as forming a perfect
square. Attention is directed to the four faces 44, 45, 46, and 47,
surrounding opposite hinges 20 and 24, the significance of which is
hereinafter set forth with respect to FIG. 10. FIG. 4 is a
right-side view of the configuration shown in FIG. 3, and indicates
tetrahedrons 9 and 10, their common hinge 21 and "corner" hinges 20
and 22.
FIG. 5 is a plan view of the configuration which results when the
configuration of FIG. 4 is "squeezed" together to close hinges 26
and 22 whereby only interior faces 28, 29, 30, and 31 can be seen.
For illustrative purposes, the figure has been rotated about
45.degree. to the left in order to bring hinge 20 to the top of the
drawing. The eight 30.degree.-60.degree.-90.degree. faces form a
large diamond having its major axis horizontal and perpendicular to
the vertical major axis of the smaller diamond formed by triangular
faces 28, 29, 30, and 31.
FIG. 6 is a plan view of the shape which results when the
configuration of FIG. 3 is turned outwardly 90.degree. (inside out)
on itself to expose interior triangular faces 28, 29, 30, 31, 32,
33, 34, and 35 to complete view, and forming an octagon as the
background figure. Interior faces 36, 37, 38, 39, 40, 41, 42, and
43, are the 30.degree.-60.degree.-90.degree. faces opposite 49, 48,
45, 44, 50, 51, 46, and 47, respectively, the latter now hidden
from view. It will be seen that these interior faces form another
four-pointed star in the foreground, and one which is shaped
differently from the star shown in FIG. 3. Again, for the purpose
of ease of illustration, the configuration is rotated about
45.degree. to the right in order to bring hinge 26 to the top of
the figure. FIG. 7 illustrates the view taken along the line 7--7
of FIG. 6.
FIG. 8 illustrates a plan view the configuration produced when that
of FIG. 6 is turned outwardly 90.degree. (inside out) on itself to
expose completely 30.degree.-60.degree.-90.degree. faces 36, 37,
38, 39, 40, 41, 42, and 43. Interior faces 52, 53, 54, 55, 56, 57,
58, and 59 form a square which appears to surround an octagon
smaller than that formed as the background by faces 36, 37, 38, 39,
40, 41, 42, and 43.
The configuration shown in plan view in FIG. 9 is produced when the
shape of FIG. 8 is "squeezed" in a manner which closes hinges 20
and 24 to conceal interior faces 52, 53, 54, 55, 56, 57, 58, and
59. When hinges 23, 25, 27 and 21 are closed, the shape illustrated
in FIG. 10 is produced. The faces of
30.degree.-60.degree.-90.degree. triangles 44, 45, 46, and 47 are
again brought into view, as are isosceles triangular faces 28, 29,
30, and 31.
Although not illustrated in the accompanying drawings, it will be
evident that the configuration of FIG. 10 is capable of further
change. For example, both wings formed by (1) faces 28, 29, 44, and
45, and (2) faces 30, 31, 46, 47, can be swung downwardly to close
hinge 22; obviously, they can be swung upwardly to close hinge 26.
Or, the halves of the wings may be swung in both directions,
opening hinges 20 and 24, thereby forming still another
configuration.
As the length of the chain of tetrahedrons is increased, whether to
form a closed loop, or a string, many more such solid shapes as
shown in FIGS. 9 and 10 are possible. Furthermore, when the shape
of the tetrahedrons is changed, say to those having two opposite
congruent and obtuse triangular faces, the forms of the many
possible configurations likewise changes. The realm of geometrical
forms opened to the child through the use of my invention would
appear to be boundless. Not only can its interchangeability be
employed to educate him with respect to various colors and their
combinations, but permits the child to exercise his limitless
imagination in "creating" his own configurations or sculptures.
* * * * *