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The polyhedron is obtained on the basis of the operation of 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 bodies are semiregular polyhedra in the sense that their faces are regular polygons, but 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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