a stellated icosahedron puzzle in accordance with the present invention as shown in fig1 , 21 , 23 and 31 has six mated together hollow octahedron assemblies 1 , and twelve hollow pyramid assemblies 2 , locating on six hollow octahedron assemblies 1 with possibilities to be rotated around each of two octahedron assembly pivot shafts 3 with precise and firm position stops every 180 degree of rotation and to be independently attached from and detached to each pivot shaft 3 . each octahedron assembly 1 is formed by two identical hollow semi octahedron parts 4 shown in fig2 , 3 a , 3 b , 24 a , 25 a . each of hollow semi octahedron part 4 , shown on fig2 , 3 a - 3 f , has two halves of hollow pivot shaft 5 , symmetrically located on two top surfaces 6 of octahedron part 4 and half way protruding outside of octahedron part 4 . each half of hollow pivot shaft 5 forms in octahedron assembly full pivot shaft 3 shown on fig3 b - 3f and has top domed end 7 with small gaps 8 , designed to make hollow pivot shaft 3 elastic to allow insertion of the pyramid assembly 2 with possibility to provide robust and easy pyramid assemblies attachments from and detachments to the puzzle . on the top surfaces 6 bumps 9 are located , shown on fig2 , 3 a - 3 d . bumps 9 provide precise and firm position stops every 180 degree of pyramid assembly rotation after insertion it into pivot shaft 5 of octahedron assembly 1 . each octahedron part 4 has on inside hollow surfaces 10 protruded pins 11 and symmetrically located pin holes 12 as shown on fig2 and 3a . protruded pins 11 and pin holes 12 provide press fit engagement of two octahedron parts 4 to form and secure one octahedron assembly 1 as shown on fig3 a , 3 b , 25 a and 25 b . each pyramid assembly 2 is formed by two identical hollow semi pyramid parts 13 shown on fig4 , 5 a , fig5 b , 26 and 27 a . each hollow pyramid part 13 has cutout 14 with domed top 15 shown on fig4 and 5a , formed for firm engagement with pivot shaft 5 . each pyramid part 13 has , on inside hollow surfaces 16 , protruded pins 17 and symmetrically located pin holes 18 as shown on fig4 and 5a . protruded pins 17 and pin holes 18 provide press fit engagement of two pyramid parts 13 to form and secure one pyramid assembly 2 as shown on fig5 a , 5 b , 27 a and 27 b . outside surfaces 19 of pyramid part 13 have small recesses 20 as shown on fig5 a - 5d for locating label inserts 21 shown on fig5 a and 5b . label inserts 21 can be pressed or glued into recesses 20 as shown on fig5 a . label inserts 21 can have different colors , or numbers , or letters , or indexes 22 as shown on fig6 a - 6e . indexes 22 are designed to identify similar by color or number , or letter surfaces on the pyramid assemblies 2 . for example , surfaces with one index are identical to the surface with the same color , number or letter . surfaces with two indexes are identical to different surface with different , from index one , another color , number or letter . indexes 22 can be protruded or recessed . protruded or recessed indexes 22 can help visually impaired people to play puzzle or simply play puzzle in a dark environment , which extends puzzle possibilities . outside surface 23 which is base bottom surface of pyramid part 13 has two symmetrical revolved cutouts 24 shown on fig4 , 5 a and 5 e designed for interaction with bumps 9 on octahedron assemblies 1 . this provides necessary position fix every 180 degree of rotation of pyramid assembly 2 on pivot shaft 3 of octahedron assembly 1 . on the bottom outside middle surface of the octahedron part 4 can be provided u - shaped groove formations 25 , shown on fig2 b , 24 d , 24 e , 25 a - 25 c and 25 e . on the bottom outside opposite surfaces of the octahedron part 4 can be provided grip formations 26 shown on fig2 c - 25e . these formations 25 and 26 can help to provide easy and secure attachment and detachment of all six octahedron assemblies 1 between themselves in puzzle assembly and help to keep octahedron assemblies 1 together much easier and more secure . engagement is shown on fig3 . for easy repeatable attachments and detachments of pyramid assemblies 2 each pyramid part 13 can have , on pyramid apex , hollow semi spheres 27 with symmetrically locating pins 17 on one side and pin holes 18 on another side with ensuring press - fit engagement , shown on fig2 and 27a . in pyramid assembly 2 these semi spheres 27 form full spheres 28 , which serve as convenient handles , shown on fig2 b - 27e and 31 . puzzle assembly process starts with mating together two octahedron assemblies 1 , shown on fig7 a and 7b . next step in assembly process is shown on fig8 a and 8b where third octahedron assembly 1 is mating together with previously assembled two octahedron assemblies 1 . following similar steps with four , five and six octahedron assemblies 1 are shown on fig9 a - 11b . player keeps all pieces together in his hands . next step is to install pyramid assemblies 2 , shown on fig1 a and 12b . continuation of the same installation steps of all pyramid assemblies 2 into puzzle is shown on fig1 and 14 . the goal is not only to assemble puzzle into stellated icosahedron , but to locate all pyramid assemblies 2 with label inserts 21 with the same indexes 22 ( or the same colors , numbers , letters ) close to each other around entire puzzle . for this step , pyramid assemblies 2 can be rotated and reoriented as shown on fig1 , detached and reattached to the new position on octahedron assembly 1 as shown on fig1 and 21 . another way how to assemble icosahedron puzzle is shown on fig1 a - 20 . following this way , first step is to assemble together two pyramid assemblies 2 with one octahedron assembly 1 into core subassembly 29 as shown on fig1 a and 16b . second step is to assemble two core subassemblies 29 together as shown on fig1 a and 17b . third step is to assemble another core subassembly 29 with previously assembled two core subassemblies 29 into large subassembly 30 as shown on fig1 a and 18b . first , second and third steps should be repeated one more time to create second large subassembly 30 shown on fig1 . it should be admitted that player has to keep all assembled subassemblies in his hands before the final stellated icosahedron puzzle is completely assembled into one piece . finally , last step is to clamp together two large subassemblies 30 into stellated icosahedron puzzle as shown in fig1 , 20 and 23 . as mentioned before , for convenient and more secure assembly all parts into puzzle octahedron parts 4 can have u - shaped groove formations 25 and grip formations 26 ; pyramid parts 13 can have semi spheres 27 .
a stellated icosahedron puzzle has a plurality of assembled together parts forming in an assembled condition a stellated icosahedron , the assemblies including six mated together hollow octahedron assemblies and twelve hollow pyramid assemblies located on the hollow octahedron assemblies rotatable around each of the octahedron assembly via pivot shafts of the octahedron assemblies and stoppable every 180 ° of rotation , and the pyramid assemblies being independently attachable to and detachable from each of the pivot shafts .