# Transformation of Icosahedral Solids in Z15

Transformation of Icosahedral Solids in Z15

This Demonstration relates the deflation of the space-filling Danzer tetrahedra, "A", "B", "C", and "K", to the transformation of three solids with full icosahedral symmetry: an icosidodecahedron, two equivalent dodecahedra, and an icosahedron. All transformations are computed in and projected into Euclidean space. Transformations that move points away from the origin are depicted as paths of connected line segments. For each transformation, the display shows only one element of the entire set of paths, which contains a number of elements equal to the factorial of the rank of the transformation.

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