Aug. 19, 1969 M. A. LARSEN ETAL 3,461,5 74 EDUCATIONAL TOY Filed July 10, 1967 '7' Sheets-Sheet 1 INVENTORS MARGET A.LARSEN B‘, EARL SICKLER ‘ ATTORNEYS. ' Alig- 19, 1969 ‘ ‘M. A. LARSEN ETAL 3,461,574 EDUCATIONAL TOY Filed July 10, 1967 7 Sheets-Sheet 2 INVEN TOR-5' MARGET A. L A RSEN Ema/MGMY EARL SICKLER ATTORNEYS Aug- 19, 1969 M. A. LARSEN ETAL 3,461,574 EDUCATIONAL TOY Filed July 10, 1967 7 Sheets-Sheet I5 FIG.2 INVENTORS MARGET A. LARSEN BlW‘q/MV EARL SICKLER ' AT TQRNEYS ' Aug-‘19, 1959 ' ,M. A. LARSEN ETAL 3,461,574 EDUCATIONAL TOY Filed July 10, 1967 . 7 Sheets-Sheet 4 MARGET ANVENTORS.LAR EA RL SICKLERSEN BYWay/WW5 ATTORNEYS Aug. 19, 1969v 3,461,574 Ill" l Aug. 19, 1969 M. A. LARSEN ETAL 3,461,574 EDUCATIONAL TOY Filed July 10, 1967 7 Sheets-Sheet 6 . INVENTORS MARGET A. LARSEN EARL SICKLER ATTORNEYS _ ‘Aug- 19, 1-969 ' M. A. LARSEN ETAL 3,451,574 EDUCAT IONAL TOY Filed July 10. 1967 7 Sheds-Sheet 7 FIG.4F INVENTORS MARGET A. LARSEN EARL SICKLER BY ' _ ATTORNEYS 3,461,574 United States Patent ‘a ice Patented Aug. 19, 1969 1 2 3,461,574 cahedron and a rhombic dodecahedron as well as a stel EDUCATIONAL TOY _ lated dodecahedron and a stellated rhombic dodeca Marget A. Larsen and Earl E. Sickler, SamFranerspo, heron. Calif., assignors to Initrinsics, Inc., San Francisco, Cah?, In accordance with another aspect of the present in cor oration of Cali ornia a p Filed July 10, 1967, Ser. No. 652,056 vention, each of the polyhedra except the smallest in Int. Cl. A6311 33/08 the series includes a pair of inter?tting members with at US. CI. 35-73 15 Claims least one member of the pair including at least two pair of intersecting walls with the lines of intersection of the two pair of walls parallel. Each wall of the two pair of ABSTRACT OF THE DISCLOSURE 10 walls of the one inter?tting member lies within a plane An educational toy including a plurality of polyhedra, parallel to a wall of the other of the inter?tting members all of different size and con?guration and all but the when the members are inter?tted together and the two smallest formed of two telescopically inter?tting mem separate members of each of the polyhedra slidably ?t bers and including in descending order of size: a hexa together when the corresponding walls of the two mem 15 hedron, a cuboctahedron, a stellated rhombic dodecahe bers are positioned parallel and the two members are moved together in a direction along the aforementioned dron, a rhombic dodecahedron, an interpenetrated hexa lines of intersection. hedron and octahedron, an octahedron, an icosahedron, a stellated dodecahedron, a dodecahedron, and a tetra Since the inter?tting members telescope rather than hedron. wedge together, this construction provides each of the 20 polyhedra which is adapted and arranged to contain a -----—-———~ smaller polyhedron with a maximum sized cavity there The present invention relates in general to polyhedra within to house the next smallest polyhedron. In this and, more particularly, to an assembly of polyhedra of manner, the number of polyhedra in the series can be different con?guration and of selectively descending sizes maximum while maintaining the variation in size between for inter?tting together. _ 25 the smallest and the largest polyhedra within reasonable Broadly stated, the present invention 1s directed to limits. an educational toy made up of a plurality of polyhedra In accordance with still another aspect of the present with each of the polyhedra of a con?guration and dimen invention, each polyhedron that is contained within the sion different from the con?guration and dimension’of next larger polyhedron in the series has at least four every other polyhedron and so arranged in descendlng 30 corresponding vertices or sides. With this construction size such that each of the polyhedra except the small large air spaces do not occur in the region between the est is dimensioned to contain the next smallest poly exterior wall surfaces of one polyhedron and the interior hedron in the series and each of the polyhedra except wall surfaces of the next larger polyhedron. the largest is dimensioned to be contained within the next In accordance with another aspect of the present in largest polyhedron in the series. All of the polyhedra vention in all the polyhedra of the preferred series ex except the smallest are formed of a plurality of tele cept the smallest and the stellated con?gurations, both scopically inter?itting members for opening and closing members of the pair include the two pair of intersecting the polyhedra to assemble it in the series. walls, and corresponding walls of the two members are closely spaced when the members are telescoped together. The present invention provides a series of polyhedra 40 for teaching the names and con?gurations of each of the In the case of the stellated polyhedra, the intersecting polyhedra in the series and relating the correspondence walls on the one member include a wall portion of the between vertices, faces and edges both to clearly show shape of the base of the stellations, and when the mem the relationship between adjoining polyhedra in the series bers are nested, this wall portion on one member lies at and teach Euler’s theorem for polyhedra which states that the base of a stellation on the other member. This con for any simple polyhedron, the number of vertices V, 45 struction gives the student an appreciation for various less the number of edges E, plus the number of faces F shapes of stellated polyhedra and in particular for the is equal to two. shape of the stellation base. For example, stellations on the rhombic dodecahedron are four-sided pyramids with a rhombus forming the base and the stellations on the do In accordance with the present invention, a series of 50 decahedron are ?ve-sided pyramids with a pentagon inter?tting polyhedra is provided which includes a number forming the base. or all of the polyhedra in the following associated order: In accordance with another aspect of the invention, hexahedron, cuboctahedron, stellated rhombic dodeca all of the inter?tting members form the polyhedra which hedron, rhombic dodecahedron, interpenetrated hexa make up the educational toy of this invention are formed hedron and octahedron, octahedron, icosahedron, stellated from ?at sheet members of the con?gurations shown in dodecahedron, dodecahedron, and tetrahedron. It will the drawing. With the ?at-sheet members, the toy can be appreciated that the series provides a full range of dif be shipped and marketed in ?at-sheet form providing a ferent shaped and modi?ed polyhedra including the five considerable saving in shipping and packaging costs. regular polyhedra, each of which is a polyhedron whose Additionally, when the assemblage of the ?at-sheet mem faces are congruent regular polygons and whose poly~ 60 bers into the interiitting members of the respective poly hedral angles are congruent and which are the tetra hedra provides an educational experience to the user. hedron, hexahedron, octahedron, dodecahedron, and This latter feature is especially applicable to those poly icosahedron. hedra which include stellations since the location of the Also, the present invention clearly illustrates how stellations and the shape of the base of the stellations polyhedra can be combined and transformed. Thus, the 65 with respect to the remainder of the stellations is made series in accordance with the preferred embodiment of the apparent. present invention includes both the hexahedron and octa Other objects, features and advantages of the present hedron as well as an interpenetration of the hexahedron invention will become apparent upon reading the fol and octahedron. Additionally, the series includes a dode lowing speci?cation and referring to the accompanying 3,461,574 3 drawings in which similar characteristics of reference of the polyhedra except the tetrahedron, the smallest of represent corresponding parts in each of the several views. the series, formed of two inter?tting members and adapted In the drawings: to closely receive the next smallest polyhedron of the FIGS. 1A—] illustrate in order of descending size the series. polyhedra in the series of polyhedra utilized in the present Referring now to FIGS. 3A-3I, there are illustrated invention; the individual members of each of the polyhedra in FIG. 2 is an elevational view of a stack containing the series of polyhedron in accordance with the present the series of polyhedra in accordance with the preferred invention and the manner in which the separate mem embodiment of the present invention; bers of each polyhedron ?t together to enclose the next FIGS. 3A-I illustrate the manner in which the two IO smallest polyhedron therewithin. inter?tting members of each of the polyhedra of the As shown in FIG. 3A, the tetrahedron 100 is a solid series utilized in the present invention ?t together with ?gure and the dodecahedron 90 is made up of two hol~ the next smallest polyhedron of the series positioned there low, open ended, inter?tting members 94 and 94'. These within; and inter?tting members 914 and 94' are constructed similar FIGS. 4A-J illustrated the ?at-sheet members from 15 to other larger polyhedra except for the stellated ver which the inter?tting members of the polyhedra shown sions and include on each member 94 or 94' two pair in FIGS. 1-3 are formed. of intersecting walls with the lines of intersection of Referring now to the drawing with particular reference the two pairs parallel and the lines of intersection on to FIGURE 1, the various views of FIGURE 1 show one of the members arranged parallel to corresponding the different polyhedra that make up the series of poly 20 lines of intersection on the other of the members so that hedra utilized in the preferred embodiment of the present the two members can be telescopically nested together.