Английская Википедия:Compound of twelve pentagrammic prisms

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Шаблон:Short description

Compound of twelve pentagrammic prisms
Файл:UC37-12 pentagrammic prisms.png
Type Uniform compound
Index UC37
Polyhedra 12 pentagrammic prisms
Faces 24 pentagrams, 60 squares
Edges 180
Vertices 60
Symmetry group icosahedral (Ih)
Subgroup restricting to one constituent 5-fold dihedral (D5)

This uniform polyhedron compound is a symmetric arrangement of 12 pentagrammic prisms, aligned in pairs with the axes of fivefold rotational symmetry of a dodecahedron.

It results from composing the two enantiomorphs of the compound of six pentagrammic prisms. In doing so, the vertices of the two enantiomorphs coincide, with the result that the full compound has two pentagrammic prisms incident on each of its vertices.

Related polyhedra

This compound shares its vertex arrangement with four uniform polyhedra as follows:

Файл:Small rhombicosidodecahedron.png
Rhombicosidodecahedron
Файл:Small dodecicosidodecahedron.png
Small dodecicosidodecahedron
Файл:Small rhombidodecahedron.png
Small rhombidodecahedron
Файл:Small stellated truncated dodecahedron.png
Small stellated truncated dodecahedron
Файл:UC36-6 pentagrammic prisms.png
Compound of six pentagrammic prisms
Файл:UC37-12 pentagrammic prisms.png
Compound of twelve pentagrammic prisms

References

Шаблон:Polyhedron-stub