Rotatable connected object

[0002] This invention relates to games such as the Rubik's cube (Trademarked) and other games.

[0003] Various devices and apparatus are known in the art for providing puzzles where pieces are rotated in various ways.

[0004] The present invention in one embodiment provides an apparatus comprising a plurality of sections together forming a rotatable connected object, which may for example be a sphere. One half of the sphere can be rotated with respect to another half of the sphere in various planes in or along various circular paths. In one embodiment the sphere has eight sections and can be rotated along any one of three different circular paths, A, B, and C.

[0005] The plurality of sections may include first, second, third, fourth, fifth, sixth, seventh, and eighth sections. Each section may be joined to an adjacent section by a connector or in one embodiment by two connectors. Each connector may allow each section to rotate with respect to other sections. A plurality of connectors including twenty-four connectors for connecting eight sections may be provided.

[0006] Each connector may be comprised of first and second curved rails and a first gear. The first gear may be connected to the first and second curved rails. Each section may be comprised of a rail channel and a gear channel. The first and second curved rails of each connector may fit into the rail channels of each section. The first gear of the each connector may fit into a combination channel comprised of a gear channel of one section and the gear channel of an adjacent section.

[0007] The first and second curved rails of each connector may be connected to a first shaft of each connector. The first gear of each connector may be a conical gear which can rotate about the first shaft of each connector. The gear channel of the each section may include ridges which interact with the first gear of each connector when the particular section is moved with respect to an adjacent section.

[0008] Each section may have a top surface. The rail channel and gear channel of each section may lie beneath the top surface of the corresponding section and within the sphere when the plurality of sections are put together to form the sphere. The connected object may have different surfaces which may make the connected sphere appear unlike a sphere on the connected object surface. However, the rail channels and gear channels will typically form an inner sphere.

[0009] In one embodiment, the sphere can be put in a first configuration where: first and second connectors join the first section to the second section; third and fourth connectors join the first section to the third section; fifth and sixth connectors join the first section to the sixth section; seventh and eighth connectors join the second section to the fifth section; ninth and tenth connectors join the second section to the fourth section; eleventh and twelfth connectors join the third section to the fourth section; thirteenth and fourteenth connector joins the third section to the seventh section; fifteenth and sixteenth connectors join the fourth section to the eighth section; seventeenth and eighteenth connectors joins the fifth section to the sixth section; nineteenth and twentieth connectors join the fifth section to the eighth section; twenty-first and twenty-second connectors joins the sixth section to the seventh section; and the twenty-third and twenty-fourth connectors joins the seventh section to the eighth section.

[0010] A half of the sphere comprised of the first, third, seventh, and sixth sections can be rotated ninety degrees along a circle A with respect to a half of the sphere comprised-of the second, fourth, eighth, and fifth sections to change the sphere from the first configuration to a second configuration. In the second configuration, the connectors along the circle A have changed in position one half of a section arc length from the first configuration. The other connectors remain in the same position with respect to the sections they connect.

[0011] A half of the sphere comprised of the first, second, fourth, and third sections can be rotated ninety degrees along a circle B with respect to a half of- the sphere comprised of the fifth, seventh, eighth, and sixth sections to change the sphere from the first configuration to a third configuration. In the third configuration, the connectors along the circle B have changed in position one half of a section arc length from the first configuration. The other connectors remain in the same position with respect to the sections they connect.

[0012] A half of the sphere comprised of the third, fourth, eighth, and seventh sections can be rotated ninety degrees along a circle C with respect to a half of the sphere comprised of the first, second, fifth, and sixth sections to change the sphere from the first configuration to a fourth configuration. In the fourth configuration, the connectors along the circle C have changed in position one half of a section arc length from the first configuration. The other connectors remain in the same position with respect to the sections they connect.

[0013] FIG. 1A shows a front perspective view of a first sphere in accordance with an embodiment of the present invention with the sphere in a first configuration;

[0014] FIG. 1B shows a rear perspective view of the sphere of FIG. 1A in the first configuration;

[0015] FIGS. 2A and 2B show front and rear perspective views of the first sphere in a second configuration;

[0016] FIGS. 3A and 3B show front and rear perspective views of the first sphere in a third configuration;

[0017] FIGS. 4A and 4B show front and rear perspective views of the first sphere in a fourth configuration;

[0018] FIGS. 5A and 5B show interior sectional views of a first half and a second half of the first sphere in the first configuration of FIG. 1 separated along circle A;

[0019] FIGS. 6A and 6B show interior sectional views of a first half and a second half of the first sphere in the first configuration of FIG. 1 separated along circle B;

[0020] FIGS. 7A and 7B show interior sectional views of a first half and a second half of the first sphere in the first configuration of FIG. 1 separated along circle C;

[0021] FIG. 8 shows an interior cross sectional view of two pieces of the first sphere joined together; and

[0022] FIG. 9 shows a bottom planar view of a connector for connecting two or more pieces of the sphere.

[0023] FIG. 1A shows a front perspective view of a first sphere 10 in accordance with an embodiment of the present invention with the first sphere 10 in a first configuration. FIG. 1B shows a rear perspective view of the first sphere 10 in the first configuration. The first sphere 10 is comprised of eight sections: 100, 200, 300, 400, 500, 600, 700, and 800. In the example of FIGS. 1A-1B, the sphere 10 could be thought of conceptually as being cut by three planes which are traversed by circles A, B, and C, respectively. In another embodiment, the first sphere 10 could be divided further into, for example, thirty-two sections by being cut conceptually by six planes, similar to a icosidodecahedron. The first sphere 10 is further comprised of twenty-four connectors: 900, 910, 920, 930, 940, 950, 960, 970, 980, 990, 1000, 1010, 1100, 1110, 1120, 1130, 1140, 1150, 1160, 1170, 1180, 1190, 1200, and 1210, which connect various sections of the sections 100 through 800 together as will be described.

[0024] The sections 100, 200, 300, 400, 500, 600, 700, and 800 of the sphere 10 in FIGS. 1A and 1B can be rotated with respect to one another in three rotational directions or dimensions as will be described. The sections 100-800 of sphere 10 can be rotated with respect to one another along the circle A, along the circle B, or along the circle C shown in FIGS. 1A and 1B. FIGS. 2A and 2B show the sphere 10 in a second configuration after half of the sphere 10 has been rotated with respect to another half of the sphere about circle A. FIGS. 3A and 3B show the sphere 10 in a second configuration after half of the sphere 10 in the configuration of FIGS. 1A-1B has been rotated with respect to another half of the sphere about circle B. FIGS. 4A and 4B show the sphere 10 in a third configuration after half of the sphere 10 in the configuration of FIGS. 1A-1B has been rotated with respect to another half of the sphere about circle C.

[0025] FIGS. 1A-4B also show poles N, E, W, S, F, and Ba.

[0026] In the first configuration of FIGS. 1A and 1B, in FIG. 1A, sections 100 and 200 are shown next to each other on the top of the sphere 10 above the circle C, while the sections 300 and 400 are shown next to each other on the bottom of the sphere 10. Sections 500 and 600 are also shown on the top of the sphere 10, while sections 700 and section 800 (shown in FIG. 1B) are on the bottom of the sphere 10. In FIG. 1A, connectors 900 and 1100 hold sections 600 and 100 together, connectors 910 and 1110 hold sections 100 and 300 together, connectors 920 and 1120 (shown by FIGS. 6A and 6B) hold sections 700 and 300 together, connectors 930 and 1130 (shown by FIGS. 5A and 5B) hold sections 300 and 400 together, connectors 940 (shown by FIGS. 6A and 6B) and 1140 hold sections 400 and 800 together (shown in FIG. 1B), connectors 950 (shown by FIG. 1B) and 1150 hold sections 200 and 400 together; connectors 960 and 1160 hold sections 500 and 200 together (shown by FIG. 1B), connectors 970 and 1170 hold sections 100 and 200 together, connectors 980 (shown in FIG. 1A) and 1180 (shown by FIG. 1B) hold sections 600 and 700 together, connectors 990 and 1190 (shown by FIG. 1B) hold sections 500 and 600 together, connectors 1000 (shown by FIGS. 5A and 5B) and 1200 (shown by FIG. 1B) holds sections 700 and 800 together (shown in FIG. 1B) and connectors 1010 and 1210 hold sections 500 and 800 together (shown by FIG. 1B).

[0027] To change the sphere 10 from the first configuration of FIGS. 1A and 1B to the second configuration of FIGS. 2A and 2B, the half of the sphere 10 including sections 600, 100, 300 and 700 is rotated ninety degrees along the circle A of FIG. 1, with respect to the half of the sphere 10 including sections 200, 400, 800, and 500. The half of the sphere 10 (sections 600, 100, 300, and 700) could be rotated any multiple of ninety degrees to form a new configuration for sphere 10, such as one hundred eighty degrees, or two hundred seventy degrees). The ninety degree rotation causes section 100 to move from the top of the sphere 10 in FIG. 1A to the bottom of the sphere 10 in FIGS. 2A and 2B, section 300 to move to the back bottom of the sphere 10 as viewed in FIGS. 2A and 2B (the back of FIG. 2A, shown in FIG. 2B), section 700 to move to the top of the sphere 10, and section 600 to move to the front top of the sphere 10 as viewed in FIG. 2A. When the sections 600, 100, 300 and 700 were rotated ninety degrees with respect to sections 200, 400, 800, and 500, the connectors along the circle A (i.e. the circular direction of rotation) were moved half the section side arc length of a section (of sections 100-800).

[0028] The section side arc length is the arc length from one pole to any of its adjacent poles. For example, the section side arc length is equal to the arc length from the pole “N” to the pole “F” in FIG. 1A. Connector 970 has a center point 976 which lies on the circle A. The center point 976 is at a distance of ¼ of the section side arc length from the north pole “N” in FIG. 1A. When sphere 10 is changed from the configuration of FIGS. 1A-1B to the configuration of FIGS. 2A-2B, the connector 970 moves so that in FIG. 2A the center point 976 is at a distance of ¼ of the section side arc length from the front pole “F”. The connector 970 has thus moved ½ of a section side arc length with the ninety degree rotation. Thus in a sense, while the sections 100, 300, 700, and 600 have moved a full section side arc length from FIGS. 1A-B to FIGS. 2A-B, the connectors along line A have only moved % of a section side arc length. Connectors 1170, 930, 1130, 1000, 1200, 990, and 1190 which are on circle A, move in a similar manner to connector 970 as shown by FIGS. 2A and 2B.

[0029] In the second configuration of FIGS. 2A and 2B, along circular line A, connectors 1190 and 970 hold sections 600 and 200 together, connectors 1170 and 930 hold sections 100 and 400 together, connectors 990 and 1200 hold sections 700 and 500 together, and connectors 1000 and 930 hold sections 300 and 800 together. The connectors along circular line A have thus changed where they are located with respect to sections that they connect and in some cases now connect different sections together. Other than the connectors along circular line A, the other connectors as shown in FIGS. 2A-2B, continue to join together the same sections that they joined together in FIGS. 1A-1B and those other connectors do not move with respect to the sections that they join together.

[0030] To change the sphere 10 from the first configuration of FIGS. 1A and 1B to the third configuration of FIGS. 3A and 3B, the half of the sphere 10 including sections-100, 200, 400 and 300 is rotated ninety degrees along the circle B of FIG. 1A, with respect to the half of the sphere 10 including sections 500, 600, 700, and 800. The half of the sphere 10 (sections 100, 200, 400, and 300) could be rotated any multiple of ninety degrees to form a new configuration for sphere 10, such as one hundred eighty degrees, or two hundred seventy degrees). The ninety degree rotation causes section 100 to move from the top left of the sphere 10 in FIG. 1A to the top right of the sphere 10 in FIGS. 3A and 3B, section 200 to move to the bottom right of the sphere 10 as viewed in FIGS. 3A and 3B, section 400 to move to the bottom left of the sphere 10, and section 300 to move to the front left of the sphere 10 as viewed in FIG. 3A. When the sections 100, 200, 400 and 300 were rotated ninety degrees with respect to sections 500, 600, 700, and 800, the connectors along the circle B (connectors 1120, 920, 1100, 900, 1160, 960, 1140, 940 (i.e. in the circular direction of rotation) were moved half a section side arc length.

[0031] In the third configuration of FIGS. 3A and 3B, along circular line B, connectors 1120 and 940 hold sections 400 and 700 together, connectors 1100 and 920 hold sections 300 and 600 together, connectors 900 and 1160 hold sections 100 and 500 together, and connectors 1140 and 960 hold sections 200 and 800 together. The connectors along circular line B have thus changed where they are located with respect to sections that they connect and in some cases now connect different sections together. Other than the connectors along circular line B, the other connectors as shown in FIGS. 3A-3B, continue to join together the same sections that they joined together in FIGS. 1A-1B and those other connectors do not move with respect to the sections that they join together.

[0032] To change the sphere 10 from the first configuration of FIGS. 1A and 1B to the third configuration of FIGS. 4A and 4B, the half of the sphere 10 including sections 300, 400, 800 and 700 is rotated ninety degrees along the circle C of FIG. 1A, with respect to the half of the sphere 10 including sections 200, 100, 600, and 500. The half of the sphere 10 (sections 300, 400, 800, and 700) could be rotated any multiple of ninety degrees to form a new configuration for sphere 10, such as one hundred eighty degrees, or two hundred seventy degrees). The ninety degree rotation causes section 700 to move to the front left of the sphere 10, section 300 to move to the bottom front right of the sphere 10, section 400 to move to the back of the sphere 10, and section 800 to move to the back right as seen in FIGS. 4A and 4B. When the sections 300, 400, 800 and 700 were rotated ninety degrees with respect to sections 200, 100, 600, and 500, the connectors along the circle C (connectors 1110, 910, 1150, 950, 1210, 1010, 1180, and 980, (i.e. in the circular direction of rotation) were moved half a section side arc length.

[0033] In the third configuration of FIGS. 4A and 4B, along circular line C, connectors 980 and 1110 hold sections 100 and 700 together, connectors 910 and 1150 hold sections 200 and 300 together, connectors 950 and 1210 hold sections 500 and 400 together, and connectors 1010 and 1180 hold sections 600 and 800 together. The connectors along circular line C have thus changed where they are located with respect to sections that they connect and in some cases now connect different sections together. Other than the connectors along circular line C, the other connectors as shown in FIGS. 4A-4B, continue to join together the same sections that they joined together in FIGS. 1A-1B and those other connectors do not move with respect to the sections that they join together.

[0034] FIGS. 5A and 5B show interior sectional views of a first half and a second half of the first sphere 10 along with the location of gears in the first configuration of FIG. 1 separated along circle A.

[0035] Along circle A, FIG. 5A shows an interior view of sections 500, 200, 400, and 800. The sections 500, 200, 400, and 800 are comprised of surfaces 510a, 210a, 410a, and 810arespectively along the circle A shown in FIG. 1A. Section 500 is comprised of a solid portion 501a, a channel opening 502a, a solid portion 503a, rail channels 513a, 513b, and 513c, and gear channel 520a, 520b, and 520c. The solid portion 501ahas a first end 530aand a second end 532a. The solid portion 503ahas a first end 534aand a second end 536a. The gear channel 520ahas a first end 540aand a second end 542a. There are a plurality of ridges 521ain the gear channel 520a. The rail channel 513ais shown in dashed lines in FIG. 5A and runs from the first end 530ato the second end 532anear the solid portion 501aand from the first end 540ato the second end 542anear the solid portion 503a.

[0036] The location of a curved rail 992 for the connector 990 is shown in dashed lines in FIG. 5A and in FIG. 1B. The curved rail 992 lies inside the section 500 in FIG. 1, and inside the channel 513a. The curved rail 992 is connected by a curved piece 995 to another curved rail 993 as shown in dashed lines in FIG. 1B. The curved piece 995 is connected to a shaft 991, shown in FIG. 5A and whose location is also shown by dashed lines in FIG. 1B. The shaft 991 is connected to a conical gear 994 which is partially shown in FIG. 5A and whose location is shown by dashed lines in FIG. 1B.

[0037] To insert the curved rail 992 into the rail channel 513a, the curved rail 992 is located parallel to the rail channel 513aand pushed through the rail opening 502a. The solid portions 501aand 503apreferably are elastic so that the rail opening 502aexpands to allow the curved rail 992 to enter the rail channel 513aand then after the curved rail 992 is within the rail channel 513a, the rail opening 502acontracts to the size shown in FIG. 5A in order to retain the curved rail 992 within the rail channel 513a(or within one of the other rail channels, as will be described, after a rotation).

[0038] Along circle A, the sections 200, 400 and 800 in FIG. 5A have portions very similar to the section 500.

[0039] Sections 200, 400, and 800 are comprised of solid portions 201a, 401a, and 801a, respectively, channel openings 202a, 402a, and 802arespectively, solid portions 203a, 403a, and 803a, respectively, rail channels 213a-c, 413a-c, and 813a-crespectively, gear channels 220a-c, 420a-cand 820a-c, respectively. The solid portions 201a, 401a, and 801ahave first ends 230a, 430a, and 830a, respectively, and second ends 232a, 432a, and 832a, respectively. The solid portions 203a, 403a, and 803arespectively have first ends 234a, 434a, 834aand second ends 236a, 436a, and 836arespectively. The gear channels 220a, 420a, and 820ahave first ends 240a, 440a, and 840arespectively, and second ends 242a, 442a, and 842a, respectively. There are a plurality of ridges 221a, 421a, and 821ain the gear channels 220a, 420a, and 820arespectively. The rail channels 213a, 413a, and 813aare shown in dashed lines in FIG. 5A and run from the first ends 230a, 430a, and 830a, respectively to the second ends 232a, 432a, and 832a, respectively, near the solid portions 201a, 401a, 801a, respectively and from the first end 240a, 440a, and 840a, respectively to the second end 242a, 442a, and 842a, respectively near the solid portions 203a, 403a, and 803a, respectively.

[0040] The location of curved rails 1192, 972, 1172, 932, 1132, 1002, and 1202, respectively for the connectors 1190, 970, 1170, 930, 1130, 1000, and 1200, respectively, are shown in dashed lines in FIG. 5A and in FIGS. 1A and 1B. Curved rail 1192 lies inside section 500 and inside channel 513a. Curved rails 972 and 1172 lie inside section 200 and inside channel 213a. Curved rails 930 and 1130 lie inside section 400 and inside channel 413a. Curved rails 1002 and 1202 lie inside section 800 and inside channel 813a. The curved rails 1192, 972, 1172, 932, 1132, 1002, and 1202, respectively are connected by curved pieces 1195, 975, 1175, 935, 1135, 1005, and 1205, respectively to another curved rail 1193, 973, 1173, 933, 1133, 1003, and 1203 as shown in dashed lines in one or both of FIGS. 1A and 1B. The curved pieces 1195, 975, 1175, 935, 1135, 1005, and 1205 are connected to shafts 1191, 971, 1171, 931, 1131, 1001, and 1201, respectively, shown in FIG. 5A and whose locations are also shown by dashed lines in FIGS. 1A and 1B. The shafts 1191, 971, 1171, 931, 1131, 1001, and 1201 are connected to conical gears 1194, 974, 1174, 934, 1134, 1004, and 1204, respectively, which is partially shown in FIG. 5A and whose location is shown by dashed lines in one or both of FIGS. 1A and 1B.

[0041] Insertion of the curved rails 1192, 972, 1172, 932, 1132, 1002, and 1202 into the rail channels 513a(1192 goes into), 213a(972 and 1172 go into), 413a(932 and 1132 go into), and 813a(1002 and 1202 go into), is similar to that described for insertion of curved rail 992 into the rail channel 513a.

[0042] FIG. 5A also shows the connectors 1160, 1150, 940, and 1010. Only a perspective portion of these connectors are shown, since they are located with their centers down ¼ of a section side arc length away from the nearest pole. For example, the center of connector 1160 is ¼ of a section side arc length away from the “N” pole or North Pole.

[0043] FIG. 5B shows sections 100, 600, 700, and 300 when the sphere 10 of the configuration of FIGS. 1A and 1B is cut along circle A. The sections 100, 600, 700, and 300 in FIG. 5B have portions very similar to those for sections 500, 200, 400, and 800 of FIG. 5A.

[0044] Sections 100, 600, 700, and 300 are comprised of solid portions 101a, 601a, 701a, and 301a, respectively, channel openings 102a, 602a, 702a, and 302arespectively, solid portions 103a, 603a, 703a, and 303a, respectively, rail channels 113a-c, 613a-c, 713a-c, and 313a-crespectively, gear channels 120a-c, 620a-c, 720a-cand 320a-c, respectively. The solid portions 101a, 601a, 701a, and 301ahave first ends 130a, 630a, 730a, and 330a, respectively, and second ends 132a, 632a, 732a, and 332a, respectively. The solid portions 103a, 603a, 703a, and 303arespectively have first ends 134a, 634a, 734a, 334aand second ends 136a, 636a, 736a, and 336arespectively. The gear channels 120a, 620a, 720a, and 320ahave first ends 140a, 640a, 740a, and 340arespectively, and second ends 142a, 642a, 742a, and 342a, respectively. There are a plurality of ridges 121a, 621a, 721a, and 321ain the gear channels 120a, 620a, 720a, and 320arespectively. The rail channels 113a, 613a, 713a, and 313aare shown in dashed lines in FIG. 5A and run from the first ends 130a, 630a, 730a, and 330a, respectively to the second ends 132a, 632a, 732a, and 332a, respectively, near the solid portions 101a, 601a, 701a, 301a, respectively and from the first end 140a, 640a, 740a, and 340a, respectively to the second end 142a, 642a, 742a, and 342a, respectively near the solid portions 103a, 603a, 703a, and 303a, respectively.

[0045] The location of curved rails 1173, 973, 1193, 993, 1203, 1003, 1133, and 933, respectively for the connectors 1170, 970, 1190, 990, 1200, 1000, 1130, and 930, respectively, are shown in dashed lines in FIG. 5B and in one or both of FIGS. 1A and 1B. Curved rail 1173 and 973 lies inside section 100 and inside channel 113a. Curved rails 1193 and 993 lie inside section 600 and inside channel 613a. Curved rails 1203 and 1003 lie inside section 700 and inside channel 713a. Curved rails 1133 and 933 lie inside section 300 and inside channel 313a. The curved rails 1173, 973, 1193, 993, 1203, 1003, 1133, and 933, respectively are connected by curved pieces 1175, 975, 1195, 995, 1205, 1005, 1135, and 935, respectively, to another curved rail 1172, 972, 1192, 992, 1202, 1002, 1132, and 932, as shown in dashed lines in one or both of FIGS. 1A and 1B. The curved pieces 1175, 975, 1195, 995, 1205, 1005, 1135, and 935 are connected to shafts 1171, 971, 1191, 991, 1201, 1001, 1131, and 931, respectively, shown in FIG. 5B and whose locations are also shown by dashed lines in one or both of FIGS. 1A and 1B. The shafts 1171, 971, 1191, 991, 1201, 1001, 1131, and 931 are connected to conical gears 1174, 974, 1194, 994, 1204, 1004, 1134, and 934, respectively, which is partially shown in FIG. 5B and whose location is shown by dashed lines in one or both of FIGS. 1A and 1B.

[0046] Insertion of the curved rails 1173, 973, 1193, 993, 1203, 1003, 1133, and 933 into the rail channels 113a(1173 and 973 go into), 613a(1193 and 993 go into), 713a(1203 and 1003 go into), and 313a(1133 and 933 go into), is similar to that described for insertion of curved rail 992 into the rail channel 513a.

[0047] FIG. 5B also shows the connectors 900, 980, 1120, and 910. Only a perspective portion of these connectors are shown, since they are located with their centers down ¼ of a section side arc length away from the nearest pole.

[0048] FIG. 6A shows sections 200, 100, 300, and 400 when the sphere 10 of the configuration of FIGS. 1A and 1B is cut along circle B. The parts of sections 200, 100, 300, and 400 as shown in FIG. 6A have portions very similar to those for FIG. 5A.

[0049] Sections 200, 100, 300, and 400 are comprised of solid portions 201b, 101b, 301b, and 401b, respectively, channel openings 202b, 102b, 302b, and 402brespectively, solid portions 203b, 103b, 303b, and 403b, respectively, rail channels 213a-c, 113a-c, 313a-c, and 413a-crespectively, gear channels 220a-c, 120a-c, 320a-cand 420a-c, respectively. The solid portions 201b, 101b, 301b, and 401bhave first ends 230b, 130b, 330b, and 430b, respectively, and second ends 232b, 132b, 332b, and 432b, respectively. The solid portions 203b, 103b, 303b, and 403brespectively have first ends 234b, 134b, 334b, 434band second ends 236b, 136b, 336b, and 436brespectively. The gear channels 220b, 120b, 320b, and 420bhave first ends 240b, 140b, 340b, and 440brespectively, and second ends 242b, 142b, 342b, and 442b, respectively. There are a plurality of ridges 221b, 121b, 321b, and 421bin the gear channels 220b, 120b, 320b, and 420b, respectively. The rail channels 213b, 113b, 313b, and 413bare shown in dashed lines in FIG. 6A and run from the first ends 230b, 130b, 330b, and 430b, respectively to the second ends 232b, 132b, 332b, and 432b, respectively, near the solid portions 201b, 101b, 301b, 401b, respectively and from the first end 240b, 140b, 340b, and 440b, respectively to the second end 242b, 142b, 342b, and 442b, respectively near the solid portions 203b,103b, 303b, and 403b, respectively.

[0050] The location of curved rails 962, 1162, 902, 1102, 922, 1122, 942, and 1142, respectively for the connectors 960, 1160, 900, 1100, 920, 1120, 940, and 1140, respectively, are shown in dashed lines in FIG. 5B and in one or both of FIGS. 1A and 1B. Curved rails 962 and 1162 lie inside section 200 and inside channel 213b. Curved rails 902 and 1102 lie inside section 100 and inside channel 113b. Curved rails 922 and 1122 lie inside section 300 and inside channel 313b. Curved rails 942 and 1142 lie inside section 400 and inside channel 413b. The curved rails 962, 1162, 902, 1102, 922, 1122, 942, and 1142, respectively are connected by curved pieces 965, 1165, 905, 1105, 925, 1125, 945, and 1145, respectively, to another curved rail 963, 1163, 903, 1103, 923, 1123, 943, and 1143, as shown in dashed lines in one or both of FIGS. 1A and 1B. The curved pieces 965, 1165, 905, 1105, 925, 1125, 945, and 1145 are connected to shafts 961, 1161, 901, 1101, 921, 1121, 941, and 1141, respectively, shown in FIG. 6A and whose locations are also shown by dashed lines in one or both of FIGS. 1A and 1B. The shafts 961, 1161, 901, 1101, 921, 1121, 941, and 1141 are connected to conical gears 964, 1164, 904, 1104, 924, 1124, 944, and 1144, respectively, which is partially shown in FIG. 6B and whose location is shown by dashed lines in one or both of FIGS. 1A and 1B.

[0051] Insertion of the curved rails 962, 1162, 902, 1102, 922, 1122, 942, and 1142 into the rail channels 213b(962 and 1162 go into), 113b(902 and 1102 go into), 313b(922 and 1122 go into), and 413b(942 and 1142 go into), is similar to that described for insertion of curved rail 992 into the rail channel 513a.

[0052] FIG. 6A also shows the connectors 970, 1110, 1130, and 950. Only a perspective portion of these connectors are shown, since they are located with their centers down ¼ of a section side arc length away from the nearest pole.

[0053] FIG. 6B shows sections 600, 500, 800, and 700 when the sphere 10 of the configuration of FIGS. 1A and 1B is cut along circle B. The parts of sections 600, 500, 800, and 700 as shown in FIG. 6B have portions very similar to those for FIG. 5A.

[0054] Sections 600, 500, 800, and 700 are comprised of solid portions 601b, 501b, 801b, and 701b, respectively, channel openings 602b, 502b, 802b, and 702brespectively, solid portions 603b, 503b, 803b, and 703b, respectively, rail channels 613a-c, 513a-c, 813a-c, and 713a-crespectively, gear channels 620a-c, 520a-c, 820a-cand 720a-c, respectively. The solid portions 601b, 501b, 801b, and 701bhave first ends 630b, 530b, 830b, and 730b, respectively, and second ends 632b, 532b, 832b, and 732b, respectively. The solid portions 603b, 503b, 803b, and 703brespectively have first ends 634b, 534b, 834b, 734band second ends 636b, 536b, 836b, and 736brespectively. The gear channels 620b, 520b, 820b, and 720bhave first ends 640b, 540b, 840b, and 740brespectively, and second ends 642b, 542b, 842b, and 742b, respectively. There are a plurality of ridges 621b, 521b, 821b, and 721bin the gear channels 620b, 520b, 820b, and 720b, respectively. The rail channels 613b, 513b, 813b, and 713bare shown in dashed lines in FIG. 6B and run from the first ends 630b, 530b, 830b, and 730b, respectively to the second ends 632b, 532b, 832b, and 732b, respectively, near the solid portions 601b, 501b, 801b, 701b, respectively and from the first end 640b, 540b, 840b, and 740b, respectively to the second end 642b, 542b, 842b, and 742b, respectively near the solid portions 603b, 503b, 803b, and 703b, respectively.

[0055] The location of curved rails 1103, 903, 1163, 963, 1143, 943, 1123, and 923, respectively for the connectors 1100, 900, 1160, 960, 1140, 940, 1120, and 920, respectively, are shown in dashed lines in FIG. 6B and in one or both of FIGS. 1A and 1B. Curved rails 1103 and 903 lie inside section 600 and inside channel 613b. Curved rails 1163 and 963 lie inside section 500 and inside channel 513b. Curved rails 1143 and 943 lie inside section 800 and inside channel 813b. Curved rails 1123 and 923 lie inside section 700 and inside channel 713b. The curved rails 1103, 903, 1163, 963, 1143, 943, 1123, and 923, respectively are connected by curved pieces 1105, 905, 1165, 965, 1145, 945, 1125, and 925, respectively, to another curved rail 1102, 902, 1162, 962, 1142, 942, 1122, and 922, as shown in dashed lines in one or both of FIGS. 1A and 1B. The curved pieces 1105, 905, 1165, 965, 1145, 945, 1125, and 925 are connected to shafts 1101, 901, 1161, 961, 1141, 941, 1121, and 921, respectively, shown in FIG. 6B and whose locations are also shown by dashed lines in one or both of FIGS. 1A and 1B. The shafts 1101, 901, 1161, 961, 1141, 941, 1121, and 921 are connected to conical gears 1104, 904, 1164, 964, 1144, 944, 1124, and 924, respectively, which is partially shown in FIG. 6B and whose location is shown by dashed lines in one or both of FIGS. 1A and 1B.

[0056] Insertion of the curved rails 1103, 903, 1163, 963, 1143, 943, 1123, and 923, into the rail channels 613b(1103 and 903 go into), 513b(1163 and 963 go into), 813b(1143 and 943 go into), and 713b(1123 and 923 go into), is similar to that described for insertion of curved rail 992 into the rail channel 513a.

[0057] FIG. 6B also shows the connectors 1190, 1210, 1000, and 980. Only a perspective portion of these connectors are shown, since they are located with their centers down ¼ of a section side arc length away from the nearest pole.

[0058] FIG. 7A shows sections 100, 200, 500, and 600 when the sphere 10 of the configuration of FIGS. 1A and 1B is cut along circle C. The parts of sections 100, 200, 500, and 600 as shown in FIG. 7A have portions very similar to those for FIG. 5A.

[0059] Sections 100, 200, 500, and 600 are comprised of solid portions 101c, 201c, 501c, and 601c, respectively, channel openings 102c, 202c, 502c, and 602crespectively, solid portions 103c, 203c, 503c, and 603c, respectively, rail channels 113a-c, 213a-c, 513a-c, and 613a-crespectively, gear channels 120a-c, 220a-c, 520a-cand 620a-c, respectively. The solid portions 101c, 201c, 501c, and 601chave first ends 130c, 230c, 530c, and 630c, respectively, and second ends 132c, 232c, 532c, and 632c, respectively. The solid portions 103c, 203c, 503c, and 603crespectively have first ends 134c, 234c, 534c, 634cand second ends 136c, 236c, 536c, and 636crespectively. The gear channels 120c, 220c, 520c, and 620chave first ends 140c, 240c, 540c, and 640crespectively, and second ends 142c, 242c, 542c, and 642c, respectively. There are a plurality of ridges 121c, 221c, 521c, and 621cin the gear channels 120c, 220c, 520c, and 620c, respectively. The rail channels 113c, 213c, 513c, and 613care shown in dashed lines in FIG. 7A and run from the first ends 130c, 230c, 530c, and 630c, respectively to the second ends 132c, 232c, 532c, and 632c, respectively, near the solid portions 101c, 201c, 501c, 601c, respectively and from the first end 140c, 240c, 540c, and 640c, respectively to the second end 142c, 242c, 542c, and 642c, respectively near the solid portions 103c, 203c, 503c, and 603c, respectively.

[0060] The location of curved rails 1112, 912, 1152, 952, 1212, 1012, 1182, and 982, respectively for the connectors 1110, 910, 1150, 950, 1210, 1010, 1180, and 980, respectively, are shown in dashed lines in FIG. 7A and in one or both of FIGS. 1A and 1B. Curved rails 1112 and 912 lie inside section 100 and inside channel 113c. Curved rails 1152 and 952 lie inside section 200 and inside channel 213c. Curved rails 1212 and 1012 lie inside section 500 and inside channel 513c. Curved rails 1182 and 982 lie inside section 600 and inside channel 613c. The curved rails 1112, 912, 1152, 952, 1212, 1012, 1182, and 982, respectively, are connected by curved pieces 1115, 915, 1155, 955, 1215, 1015, 1185, and 985, respectively, to another curved rail 1113, 913, 1153, 953, 1213, 1013, 1183, and 983, as shown in dashed lines in one or both of FIGS. 1A and 1B. The curved pieces 1115, 915, 1155, 955, 1215, 1015, 1185, and 985 are connected to shafts 1111, 911, 1151, 951, 1211, 1011, 1181, and 981, respectively, shown in FIG. 7A and whose locations are also shown by dashed lines in one or both of FIGS. 1A and 1B. The shafts 1111, 911, 1151, 951, 1211, 1011, 1181, and 981 are connected to conical gears 1114, 914, 1154, 954, 1214, 1014, 1184, and 984, respectively, which is partially shown in FIG. 7A and whose location is shown by dashed lines in one or both of FIGS. 1A and 1B.

[0061] Insertion of the curved rails 1112, 912, 1152, 952, 1212, 1012, 1182, and 982 into the rail channels 113c(1112 and 912 go into), 213c(1152 and 952 go into), 513c(1212 and 1012 go into), and 613c(1182 and 982 go into), is similar to that described for insertion of curved rail 992 into the rail channel 513a.

[0062] FIG. 7A also shows the connectors 1170, 960, 990, and 1000. Only a perspective portion of these connectors are shown, since they are located with their centers down ¼ of a section side arc length away from the nearest pole.

[0063] FIG. 7B shows sections 400, 300, 700, and 800 when the sphere 10 of the configuration of FIGS. 1A and 1B is cut along the circle C. The parts of sections 400, 300, 700, and 800 as shown in FIG. 7B have portions very similar to those for FIG. 5A.

[0064] Sections 400, 300, 700, and 800 are comprised of solid portions 401c, 301c, 701c, and 801c, respectively, channel openings 402c, 302c, 702c, and 802crespectively, solid portions 403c, 303c, 703c, and 803c, respectively, rail channels 413a-c, 313a-c, 713a-c, and 813a-crespectively, gear channels 420a-c, 320a-c, 720a-cand 820a-c, respectively. The solid portions 401c, 301c, 701c, and 801chave first ends 430c, 330c, 730c, and 830c, respectively, and second ends 432c, 332c, 732c, and 832c, respectively. The solid portions 403c, 303c, 703c, and 803crespectively have first ends 434c, 334c, 734c, 834cand second ends 436c, 336c, 736c, and 836crespectively. The gear channels 420c, 320c, 720c, and 820chave first ends 440c, 340c, 740c, and 840crespectively, and second ends 442c, 342c, 742c, and 842c, respectively. There are a plurality of ridges 421c, 321c, 721c, and 821cin the gear channels 420c, 320c, 720c, and 820c, respectively. The rail channels 413c, 313c, 713c, and 813care shown in dashed lines in FIG. 7B and run from the first ends 430c, 330c, 730c, and 830c, respectively to the second ends 432c, 332c, 732c, and 832c, respectively, near the solid portions 401c, 301c, 701c, 801c, respectively and from the first end 440c, 340c, 740c, and 840c, respectively to the second end 442c, 342c, 742c, and 842c, respectively near the solid portions 403c, 303c, 703c, and 803c, respectively.

[0065] The location of curved rails 953, 1153, 913, 1113, 983, 1183, 1013, and 1213, respectively for the connectors 950, 1150, 910, 1110, 980, 1180, 1010, and 1210, respectively, are shown in dashed lines in FIG. 7B and in one or both of FIGS. 1A and 1B. Curved rails 953 and 1153 lie inside section 400 and inside channel 413c. Curved rails 913 and 1113 lie inside section 300 and inside channel 313c. Curved rails 983 and 1183 lie inside section 700 and inside channel 713c. Curved rails 1013 and 1213 lie inside section 800 and inside channel 813c. The curved rails 953, 1153, 913, 1113, 983, 1183, 1013, and 1213, respectively, are connected by curved pieces 955, 1155, 915, 1115, 985, 1185, 1015, and 1215, respectively, to another curved rail 952, 1152, 912, 1112, 982, 1182, 1012, and 1212 as shown in dashed lines in one or both of FIGS. 1A and 1B. The curved pieces 955, 1155, 915, 1115, 985, 1185, 1015, and 1215 are connected to shafts 951, 1151, 911, 1111, 981, 1181, 1011, and 1211, respectively, shown in FIG. 7B and whose locations are also shown by dashed lines in one or both of FIGS. 1A and 1B. The shafts 951, 1151, 911, 1111, 981, 1181, 1011, and 1211 are connected to conical gears 954, 1154, 914, 1114, 984, 1184, 1014, and 1214 respectively, which is partially shown in FIG. 7B and whose location is shown by dashed lines in one or both of FIGS. 1A and 1B.

[0066] Insertion of the curved rails 953, 1153, 913, 1113, 983, 1183, 1013, and 1213 into the rail channels 413c(953 and 1153 go into), 313c(913 and 1113 go into), 713c(983 and 1183 go into), and 813c(1013 and 1213 go into), is similar to that described for insertion of curved rail 992 into the rail channel 513a.

[0067] FIG. 7B also shows the connectors 930, 920, 1200, and 1140. Only a perspective portion of these connectors are shown, since they are located with their centers down ¼ of a section side arc length away from the nearest pole.

[0068] Each combination channel that a connector moves through, such as for example the combination channel comprised of channels 220band 120bshown at the top of FIG. 6A, has a first width D1 which narrows to a smaller width D4 as shown in FIG. 8. FIG. 8 is a cross sectional view of sections 100 and 200 and the connector 970 along line D in FIG. 4A. The conical gears, such as conical gear 974 shown in FIG. 8, fit snugly in this gap so that each conical gear interacts with the ridges on both sides of the combination channel that it moves in. For example, conical gear 974 shown in FIG. 8, interacts with the ridges on both channel 220band channel 120b. This interaction causes the gear 974 to rotate. When one section is moved with respect to an adjacent section, the gears of the connectors connecting the sections rotate and the curved rails, such as curved rails 972 and 973 in FIG. 8, slide in the rail channels, such as rail channels 213band 113brespectively.

[0069] Similarly, in FIG. 5A, for example, gear 1164 interacts with ridges of channels 520band 220b; gear 1154 interacts with ridges of channels 220cand 420c; gear 944 interacts with ridges of channels 420band 820b; and gear 1014 interacts with ridges of channels 520cand 820c. In FIG. 5B, for example, gear 904 interacts with ridges of channels 120band 620b; gear 984 interacts with ridges of channels 620cand 720c; gear 1124 interacts with ridges of channels 720band 320b; and gear 914 interacts with ridges of channels 120cand 320c. In FIG. 6A, for example, gear 974 interacts with ridges of channels 220band 120b; gear 1114 interacts with ridges of channels 120cand 320c; gear 1134 interacts with ridges of channels 420band 320b; and gear 954 interacts with ridges of channels 220cand 420c. In FIG. 6B, for example, gear 1194 interacts with ridges of channels 620band 520b; gear 1214 interacts with ridges of channels 520cand 820c; gear 1004 interacts with ridges of channels 720band 820b; and gear 984 interacts with ridges of channels 620cand 720c. In FIG. 7A, for example, gear 1174 interacts with ridges of channels 120aand 220a; gear 964 interacts with ridges of channels 220band 520b; gear 994 interacts with ridges of channels 620band 520b; and gear 1004 interacts with ridges of channels 120cand 620c. In FIG. 7B, for example, gear 934 interacts with ridges of channels 420aand 320a; gear 924 interacts with ridges of channels 320band 720b; gear 1204 interacts with ridges of channels 820band 720b; and gear 1144 interacts with ridges of channels 420cand 820c.

[0070] FIG. 9 shows a bottom planar view of the connector 970 for connecting two sections 100 and 200 in the FIG. 1A configuration of the sphere 10. FIG. 9 shows a bottom view of curved rails 972 and 973, a bottom view of shaft 971, a bottom view of conical gear 974, and a bottom view of curved piece 975.

[0071] The surface of a section, such as a section 100, although shown with a certain shape in the drawings, may vary in shape, as well as in color.