US3662486A - Polyhedral amusement and educational device - Google Patents

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* 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.

Description

United States Patent Freedman 51 May 16, 1972 Edward J. Freedman, 532 Madison Avenue, Glencoe, Ill. 60022 [22] Filed: Feb. 4, 1970 [21] Appl.No.: 8,510

[72] Inventor:

[52] U.S. Cl. ..46/l R, 273/155 [5 l Int. Cl. ..A63h 33/00 [58] Field of Search ..46/ l 23, 24, 24, 26, 30, 31; 35/72; 273/155 [56] References Cited UNITED STATES PATENTS 2,776,521 7/196] Zimmerman "46/25 2,992,829 l/ l 957 Hopkins ..46/26 Primary Examiner-Robert Peshock Att0rneyRobert W. Erickson [57] 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 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.

6 Claims, 10 Drawing Figura PATENTEDMM 16 1972 3,662,486

SHEET 1 BF 3 lA/l/E/V TOR: Edward J. Freedman mizuz 44. 6M,

' ATTORNEY PATENTEUMM 16 I972 SHEET 2 [IF 3 //VVNTOR Edward J Freedman A TTO/PNEY PATENTEDMM 16 I972 3, 662,486

sum 3 OF 3 INVENTOR- Edward J. Freedman A T TOR/V5) POLYHEDRAL AMUSEMENT AND EDUCATIONAL DEVICE 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 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 ofgeometrical 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 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 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 numberi.e., 4, 6, 8, l0, l2, l4, 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 triangles, obtuse triangles, or acute triangles, with the 90 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 triangles, for example, 3060-90 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 l) tetrahedrons having all congruent, isosceles faces, or 2) tetrahedrons having two congruent 30-6090 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-Le, from 306090 tetrahedronswhere one edge is 1 inch in length (the 90 edge) and the opposite edge (the edge common to the isosceles triangular faces) is 1% 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. Where the series is formed from tetrahedrons having two opposite congruent 30-6090 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 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, or one-half a phase, the latter being herein considered to be 90. Eight such connected pyramids will form the closed loop capable of continuously revolving through the 360 cycle, or four 90 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 cycle. A series of four can revolve 90, stopping short of 180; six will go through 180, but stops short of 270"; whereas, eight obtuse tetrahedrons will close and stop short of a complete 360 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 (I) 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 puzz1e" 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 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 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. I

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 30-6090 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, there being four primary 90 phases. It must be stated, however, that, during any given 90 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 -60-90 tetrahedrons.

FIG. 1 is a perspective view of two separated 3060-90 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 aclosed loop, constructed from eight 30-6090 tetrahedrons, as it appears to the viewer in one stage of the 360 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 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, 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.

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 30-60-90 tetrahedrons, 9 and 10, in perspective. Tetrahedron 9 is equipped on the 90 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 halfof a hinge element 2 null on its edge, EF, and a male half of a hinge element 3 on its opposite edge, GB. 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 GI-I.

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 edge, while the other tetrahedron 10 has the male half on its 90 edge.

FIG. 2 presents three 90 trihedrons, 11, 12, and 13, and indicates that the triangular faces, 14, l5, 16, 17, 18, and 19, are curvilinear. With respect to trihedron 1 1, the 90 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 edge, MN. It should be noted that both points J and 0 lie in planes which are perpendicular to the planes-containing 90 edges KL and MN, respectively. Points .1 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 edge QR. It will be readily ascertained that the joint formed by hinge elements 8 and 5 rotates on a 90 axis with respect to the joint formed by mating hinge elements 6 and 7.

In FIG. 1, hinge element halves l 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 edges in FIG. 1 and on the 90 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 306090 tetrahedrons, as it appears to the viewer at one stage, or phase of a complete 360 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 306090 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 comer 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 to the left in order to bring hinge 20 to the top of the drawing. The eight 3060-90 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 (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 306090 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 fourpointed 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 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 (inside out) on itself to expose completely 306090 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. is produced. The faces of 30-60-90 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 (l) 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.

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 triangles.

6. The device of claim 5 further characterized in that said faces are 3060-90 triangles.

Claims (6)

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* triangles.

6. The device of claim 5 further characterized in that said faces are 30*-60*-90* triangles.

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