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A polyhedron is obtained by successively cutting off each of the vertices of the icosahedron or dodecahedron.

The icosododecahedron is a semi-regular convex 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 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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