A polyhedron is obtained by transform into the rhombicosidodecahedron (for more detail, No. 29 of the Magic Edges).
The snub dodecahedron is a semiregular polyhedron with two properties:
1. All faces are regular polygons of two types - a pentagon and a triangle;
2. For any pair of vertices, there is a symmetry of the polyhedron (that is, a motion that translates the polyhedron into itself) that transforms one vertex to another.
Archimedean solids are semiregular polyhedra because their faces are regular polygons. Still, they are not the same, while the condition of one of the types of spatial symmetry (tetrahedral, octahedral or icosahedral) is preserved.
The polyhedron can be made in one of the other options - the snub dodecahedron having a twist to the left and having a twist to the right.
snub dodecahedron twisted to the left
snub dodecahedron twisted to the right
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