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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.

Archimedean solids are semiregular polyhedra in the sense that 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.

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