US3611620A - Rhombic hexahedra blocks for making rhombic dodecahedra and rhombic triacontahedra - Google Patents

Abstract

THE APPLICATION DISCLOSES GEOMETRIC TOY BLOCKS IN THE SHAPE OF RHOMBIC HEXAHEDRA. FOUR OBTUSE HEXAHEDRA WITH FACE VERTICES OF 109*28''17" FIT TOGETHER TO MAKE MANY GEOMETRIC SHAPES INCLUDING THE RHOMBIC DODECAHEDRON. TEN ACUTE HEXAHEDRA AND TEN OBTUSE HEXAHEDRA WITH FACE VERTICES OF 116*33''54 FIT TOGETHER TO MAKE MANY GEOMETRIC SHAPES INCLUDING THE RHOMBIC TRIACONTAHEDRON. THE HEXAHEDRON BLOCKS HAVE ATTACHING MEANS, PREFERABLY AS SHOWN IN PAT. NO. 3,413,752, FOR ATTACHING THE BLOCKS TOGETHER IN FACE TO RELATION, IN THIS SITUATION THE BLOCKS ARE MADE WITH TWO GROUP OF THREE FACES EACH INTEGRALLY FORMED AND JOINED AT THEIR COMMON VERTEX TO THE STEMS OF THE LATCHES WHICH EXTEND THROUGH THE THREE FACES OF THE OTHER GROUP.

Description

Qct. 12, 3971 c. o. PERRY 3,611,612

RHOMBIC HEXAHEDRA BLOCKS FOR MAKING RHOMBIC DODECAHEDRA AND RHOMBIC TRIACONTAHEDRA Filed June 2, 1969 3 Sheets-Sheet 1 0M2a 12, 1971 o PERRY FOR MAKING RH M RHOMBIC HL-IXAHBDRA BL 5 AND RHOMBIC TRIACONTAHE Filed June 2, 1969 3 Sheets-Sheet 3 IC DODECAHEDR INVENTOR, HARLES 0. PERRY v I r J j ATTKNEYS Uct. 12, 1971 c. 0. PERRY 3,61%2

RHOMBIC HEXAHEDRA BLOCKS FOR MAKING RHOMBIC DODECAHEDRA AND RHOMBIG TRIACONTAHEDRA Filed June 2, 1969 3 Sheets-Sheet 5 I N VNTOR. L55 0. PERRY United States Paten 3,611,620 RHOMBIC HEXAHEDRA BLOCKS FOR MAKING RHOMBIC DODECAHEDRA AND RHOMBIC TRIACONTAHEDRA Charles 0. Perry, 14 Via llppolito lPindemonte, 00152 Rome, Italy lFiled June 2, 1969, Ser. No. 829,691 Int. Q1. A6311 33/08 US. C]. 46-25 12 Claims ABSTRACT OF THE DISCLOSURE This application discloses geometric toy blocks in the shape of rhombic hexahedra. Four obtuse hexahedra with face vertices of 10928'17" fit together to make many geometric shapes including the rhombic dodecahedron. Ten acute hexahedra and ten obtuse hexahedra with face vertices of 11633'54" fit together to make many geometric shapes including the rhombic triacontahedron. The hexahedron blocks have attaching means, preferably as shown in Pat. No. 3,413,752, for attaching the blocks together in face to face relation; in this situation the blocks are made with two groups of three faces each integrally formed and joined at their common vertex to the stems of the latches which extend through the three faces of the other group.

An asexual snap fastener is shown in my US. Pat. No. 3,413,752 for attaching two bodies together. This fastener includes a stem mounted in a recess in a body with a spherical latch portion projecting partially outside of the recess for latching engagement with an identical fastener on another body. In some situations it is difiicult to manufacture toy blocks using the snap fastener of my patent because of the inconvenience of attaching individual latch stems in individual recesses in the block.

I have now found that building blocks may be made very easily with the snap fastener of my above-mentioned patent where the block has the shape of a rhombic hexahedron. When the block has this shape, the stems for the latches in three faces of the block approach each other near the common vertex of the other three faces. For this reason, blocks of this shape can be made by integrally forming (as by injection molding) three of the six faces of the hexahedron and anchoring to the common vertex of those faces the three latch stems which extend through the other three faces. The three stems are preferably integrally formed together (as by injection molding either together vw'th or separate from the three faces to which they are to be attached). The hexahedron block is then formed by attaching two of these subassemblies together.

The rhombic hexahedron blocks have not only the advantage of simplicity of manufacture, but also advantages in the variety of shapes which can be made from them. The blocks may be made with a variety of different rhombic sides, but three specific rhombic sides are preferred for three different block shapes because of the ability of blocks with those sides to fit together with other blocks.

Thus the three different kinds of blocks which are preferred are the following:

BLOCK A This is the obtuse rhombic hexahedron which has dihedral angles of 60 and 120. All six faces of the block have the shape of a rhombus with vertex angles of 3,611,620 Patented Oct. 12, 1971 10928'17 and 31'43", and the six faces are arranged with three of the obtuse angles of 10928'17" meeting in each of two vertices of the hexahedron. At the remaining four vertices of the hexahedron, two of, the acute angles of 703l'43 meet one of the obtuse angles of 10928'17".

BLOCK B:

This is the obtuse rhombic hexahedron which has dihedral angles of 36 and 144". A11 six faces of the block have the shape of a rhombus with vertex angles of 11633'54" and 63 26'06", and the six faces are arranged with three of the obtuse angles of 11633'54" meeting in each of two vertices of the hexahedron.

BLOCK C This is the acute rhombic hexahedron mate to block B. It has six faces each having the shape of a rhombus with vertex angles of 11633'54" and 6326'06", and the six faces are arranged with three of the acute angles of 6326'06" meeting in each of two vertices of the hexahedron. This rhombic hexahedron has dihedral angles of 72 and 108 and interfits with block 13 in a unique manner because both blocks have identical faces and they have dihedral angles which are one, two, three and four times 36 which is itself an integral divisor of 360.

Four blocks having the shape of block A will interfit to form a rhombic dodecahedron and may be joined to additional blocks to form columns, concave solids and a wide variety of additional geometric shapes. Additional rhombic dodecahedra can be added to 'fill space extending in any direction.

Two blocks having the shape of block C will interfit with two blocks having the shape of block B to form an irregular rhombic dodecahedron. Three of blocks B and three of blocks C may then be added to the irregular rhombic dodecahedron to make a twenty-sided rhombic solid. These six added blocks are arranged with a concave interior which engages the exterior of the irregular rhombic dodecahedron and has two concave vertices where two 108 dihedral angles meet a 144 dihedral angle and one concave vertex where one 144 dihedral angle meets three 72 dihedral angles.

The twenty sided rhombic solid made in this way has two convex vertices where the acute angles of 6326 of five rhombic faces meet. Five blocks of block C may be placed on these five faces to form a new convex vertex where five sides meet, and then the five concave areas of the resulting assembly can be filled with five blocks of block B to form an assembly of ten blocks B and ten blocks C which have the shape of a perfect convex rhombic triacontahedron (thirty rhombic faces). In this triacontahedron, all of the adjacent rhombic hexahedra are in full face to face engagement, and the triacontahedron may be extended in all directions by adding additional blocks.

As indicated above, it is preferred that the rhombic hexahedra blocks of this invention are provided with the snap fasteners of my above-mentioned patent at the center of every face. Other means may be used, however, for attaching the hexahedra together. Additionally, the hexahedra of this invention may be used for purposes other than toy building blocks. Thus, the rhombic hexahedra can be employed as containers for merchandise and for other purposes where it may be desirable to fill space with non-cubic shapes.

Other features and advantages of the invention will become apparent from the following description of specific embodiments of this invention read in conjunction with the attached drawings in which:

FIG. 1 is a perspective view of a toy block constructed in accordance with the principles of; this invention and having the shape of an obtuse rhombic hexahedron;

FIG. 2 is a side elevation of a block like the block shown in FIG. 1;

FIG. 3 is a plan view of one face of Block A mentioned above constructed as illustrated in FIG. 1;

FIG. 4 is a perspective view of a rhombic dodecahedron constructed of four blocks of FIGS. 1-3 illustrating three of said blocks exploded out of the dodecahedron;

FIG. 5 is an exploded view of the block of FIG. 1 illustrating the method of making the same;

FIG. 6 is a sequential fragmentary view illustrating the manner in which the face latches of the block of FIG I 'operate in latching two blocks together;

FIG. 7 is a perspective view of a rhombic triacontahedron constructed of blocks B and C as described above;

FIG. 8 is a plan view of one face of the blocks B and C mentioned above, and

FIG. 9 is a perspective view of five of the blocks C described above from which the tricontahedron may be made with this figure illustrating on one block the latch members of my above-mentioned patent.

Referring now to the drawings and particularly to FIGS. 1-3, a block constructed in accordance with this invention includes six rhombic face panels 10, 12, 14, 16, 18 and 20 where each panel has the shape illustrated in FIG. 3 with obtuse angles 22 and acute angles 24 which are equal respectively to 10928'17" and 703143. The face panels are joined together so that an obtuse angle 22 of each of the face panels 10, 12 and 14 meet at a hexahedron vertex 26, and an obtuse angle 22 of each of the face panels 16, 18 and 20 meet at a second hexahedron vertex 28. It will be noted that the term hexahedron vertex refers to a point of the hexahedron where three faces meet. At the remaining vertices of the hexahedron, one of the obtuse angles 22 of one face panel (14 for instance) meets two acute angles 24 of two other face panels (16 and 20 in this example). The dihedral angle between face panels and 12 is 120, and this angle is measured in a plane perpendicular to the edge 30 between the face panels 10 and 12. The dihedral angle between faces 12 and 20 is 60 and is measured in a plane perpendicular to the edge 32 Which joins these two faces.

As best illustrated in FIG. 1, each of the six faces 10 20 has a circular opening 34 at the center of the face, and a latching device such as that shown in my above-mentioned patent projects through each opening 34 with the latching device including a spherical end portion 36 and a stem 38 which cooperate with the recessed walls 34 as described in greater detail in the above-mentioned patent. In this regard, the latching sequence illustrated in FIG. 6 indicates the manner in which the latching mechanism 34-38 operates to attach two of the blocks together face to face while permitting each face of one of the blocks to be latched to any one of the six faces of the other block. As explained in thepatent, the latch is releasable permitting the blocks to be separated and rejoined in any other configuration.

The manner in which four of the blocks of FIGS. 1-3 may be joined together in a rhombic dodecahedron is illustrated in FIG. 4 where three blocks 40, 42 and 44 are latched together with one of the obtuse vertices 26 or 28 of each block located at the center of the dodecahedron as indicated at 46. A fourth identical block which is not visible in FIG. 4 completes the bottom of the dodecahedron with one of the obtuse vertices 26 or 28 located at the center 46 of the dodecahedron. It will be noted that the dodecahedron contains face centered latch portions on all of its exterior rhombic faces in addition to the latch portions on interior faces which hold the blocks together. For this reason, additional identical blocks can 4 be added to the dodecahedron to create an endless variety of additional geometric shapes.

Referring now to FIG. 5, the block of FIG. 1 is made from four pieces 48, 50, 52 and 54, each of which is made in a single integral piece preferably by injection molding. The piece 48 contains the three rhomic faces 16, 18 and 20 together with a pedestal 56 located at the vertex 28. The piece 50 is substantially identical to the piece 48 though it should be noted that the pieces can be slightly different in size if desired. Thus, the edges 58 of each of the face panels 16, 18 and 20 are beveled so that they meet at a single edge with the face panels 10, 12 and 14. However, the face panels 16, 18 and 20 may be made smaller than the face panels 10, 12 and 14 where the two pieces 48 and 50 are to be butt jointed instead of mitered.

The piece 52 contains the three stems 38 and spherical portion 36 which are designed to project through the openings 34 in the face panels 1 6, 18 and 20, and the piece 52 is mounted on the pedestal inside piece 50 at the vertex- 26. Similarly, the piece 54 contains latching members which are designed to project through openings in the face panels 10-14, and the piece 54 is mounted on pedestal 56 inside piece 48. The pieces 48 and 54 may be integrally formed together in a single molding operation, but preferably, they are separately molded as the two integral pieces and cemented together in any suitable means to anchor the piece 54 at the vertex 28.

FIG. 7 illustrates a rhombic triacontahedron which is made from a plurality of the blocks B and C mentioned above where the acute hexahedra blocks C mentioned above are denoted by the numeral 60 and the obtuse hexahedra blocks B mentioned above are denoted by numeral 62. It may be noted that the blocks which are visible in FIG. 7 are the five blocks C and five blocks B which are added to the twenty-sided rhombic solid in the final stage of making the triacontahedron where the triacontahedron is made in the sequence of steps described above.

The five acute hexahedron blocks 60 of FIG. 7 are illustrated in greater detail in FIG. 9. Each of the faces of each of the blocks 60 and 62 has a pair of obtuse vertices 64 equal to 11633'54" and a pair of acute vertices 66 equal to 63 2606". In the acute hexahedron 60 illustrated in FIG. 9, three faces 68, 70 and 72 are arranged with their acute vertices 66 meeting at a hexahedron vertex 74. The remaining three faces 76, 78 and 80 are arranged so that each one has an acute vertex 66 meeting the others at hexahedron vertex 82. The remaining vertices 84 of the acute hexahedron 60 are defined Where two obtuse vertices 64 of two faces (for instance 68 and 72) meet one acute vertex 66 of a third face (80 in this example).

In a manner similar to that illustrated in FIG. 5, the

latch balls 36 and 38 for one set of three faces are anchored to an opposite vertex of the hexahedron, and similarly, the latch means for the remaining three sides are anchored at a single vertex. In this situation, the vertices at which the latch members are anchored are two of the vertices 84.

While certain specific embodiments of the invention have been illustrated as the best mode which I contemplate for making and using the invention, it will be obvious that many modifications may be made and additional geometric figures of a wide variety can be made by the addition of additional components to the specific blocks illustrated and described above.

I claim:

1. A toy block adapted to be connected face to face to other identical blocks which comprises:

(A) six rhombic face portions connected together in the shape of a rhombic hexahedron with said hexahedron having two opposite hexahedron vertices and with each of said face portions having a central aperture therethrough, and;

(B) a latch means for each of said face portions extending from the central aperture in such face portion to a location adjacent to the one of said two hexahedron vertices opposite to said face portion with said latch means from the sets of three of said face portions forming respective ones of said vertices being anchored to each other and to said hexahedron at the other of said vertices.

2. The toy block of claim 1 characterized further in that:

(A) each of said face portions has vertex angles of substantially 10928 and 7032, and

(B) said hexahedron is an obtuse hexahedron with three of said vertex angles of 10928 meeting at each of said two hexahedron vertices and with dihedral angles of 60 and 120.

3. The toy block of claim 2 characterized further by the inclusion of three additional blocks of identical construction with said four blocks connected together in face to face relation in the shape of a rhombic dodecahedron and with the latch means at the adjacent faces of adjacent hexahedra latched with each other.

4. The toy block of claim 1 characterized further in that:

(A) each of said face portions has vertex angles of 11634 and 6326 and (B) said hexahedron is an obtuse hexahedron with three of said vertex angles of 11634 meeting at each of said two hexahedron vertices and with dihedral angles of 114 and 36.

5. A toy block of claim 1 characterized further in that:

(A) each of said face portions has vertex angles of 11634' and 6326, and

(B) said hexahedron is an acute hexahedron with two of said vertex angles of 11634' and one of said vertex angles of 6326 meeting at each of said two hexahedron vertices and with dihedral angles of 72 and 108.

6. The toy block of claim 5 characterized further by the inclusion of nine additional blocks of identical construction and ten of said blocks of claim 4 with said twenty blocks connected together in face to face relation in the shape of a rhombic triacontahedron and with the latch means at the adjacent faces of adjacent hexahedra latched with each other.

7. The toy block of claim 1 characterized further in that the three of said face portions which meet at each of said two hexahedron vertices are integrally formed as a single piece and the three of said latch means which are anchored to each other are integrally formed as a singlepiece.

8. The toy block of claim 1 characterized further in that each of said latch means comprises a generally spherical portion positioned partially within the central aperture in one of said face portions and projecting outwardly from said hexahedron by a distance greater than the radius but less than the diameter of said spherical portion and a stem smaller in diameter than said spherical portion and extending from said face portion to one of said two hexahedron vertices.

9. An assembly of toy blocks adapted to be rearranged into a plurality of geometric figures which comprises:

(A) four blocks with each block having (1) the shape of an obtuse rhombic hexahedron (2) six rhombic faces with vertex angles of 109 28' and 32 (3) said six faces arranged with three of the 10928 vertex angles thereof meeting at each of two hexahedron trihedral vertices, and

(B) attaching means for releasably attaching said four blocks in the shape of a rhombic dodecahedron with one of said hexahedron vertices of each of said four blocks meeting a said trihedral vertex of each of the others at the center of said dodecahedron.

10. The assembly of claim 9 in which said attaching means comprises identical latch means in the center of every face of every one of said blocks.

11. An assembly of toy blocks adapted to be rearranged into a plurality of geometric figures which comprises:

(A) ten blocks with each block having (1) the shape of an obtuse rhombic hexa'hedron 2) six rhombic faces with vertex angles of 11634' and 6326 (3) said six faces arranged with three of the 11634' vertex angles thereof meeting at each of two *hexahedron vertices (B) ten other blocks with each of said other blocks having (1) the shape of an acute rhombic hexahedron (2) six rhombic other block faces with vertex angles of 11634 and 6326 (3) said six other block faces arranged with three of said 6326 vertex angles thereof meeting at each of two hexahedron vertices, and

(C) attaching means for releasably attaching said twenty blocks together in face to face relation in the shape of a rhombic triacontahedron.

12. The assembly of claim 11 in which said attaching means comprises identical latch means in the center of every face of every one of said blocks.

References Cited OTHER REFERENCES Cundy et al., Mathematical Models, 2nd ed., pub. Oxford Univ. Press, 1962; pp. 116, 120 and 121 are speci fically relied upon.

F. BARRY SHAY, Primary Examiner US. Cl. X.R. 52-81

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