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The polyhedron is obtained based on the mathematical expansion (for more detail, No. 31 of the Magic Edges).
A truncated icosidodecahedron is a semiregular convex polyhedron with two properties:
1. All faces are regular polygons of three types - a decagon, a hexagon, 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.
The truncated icosidodecahedron is one of the 13 solids of Archimedes.
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