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Besides the cube and the rhombic dodecahedron, the only other polyhedron that can be totally enclosed by a symmetrical arrangement of sticks is the 30-faced triacontahedron (Fig. 151).
Fig. 151
An obvious approach to exploring the geometry of the triacontahedron for practical applications is to refer back to the previous chapters in which the mating surfaces of the puzzle pieces corresponded to faces of the rhombic dodecahedron and see which designs can be carried forward by analogy into this new geometry. Straight away, one finds that there is nothing equivalent to the diagonal burr in triacontahedral geometry, so none of the designs described in Chapters 7 through 12 have triacontahedral offspring.
Thirty Pentagonal Sticks and Dowels
Pentagonal Sub-Units
Notched Pentagonal Sticks
Notched Rhombic Sticks
The Jupiter Puzzle
The Dislocated Jupiter Puzzle
A Scrambled Jupiter?
The Dissected Triacontahedron
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