Small dodecicosidodecahedron


In geometry, the small dodecicosidodecahedron is a nonconvex uniform polyhedron, indexed as U33. It has 44 faces, 120 edges, and 60 vertices. Its vertex figure is a crossed quadrilateral.

Related polyhedra

It shares its vertex arrangement with the small stellated truncated dodecahedron and the uniform compounds of 6 or 12 pentagrammic prisms. It additionally shares its edge arrangement with the rhombicosidodecahedron, and with the small rhombidodecahedron.

Rhombicosidodecahedron
Small dodecicosidodecahedron
Small rhombidodecahedron

Small stellated truncated dodecahedron
Compound of six pentagrammic prisms
Compound of twelve pentagrammic prisms

Dual

The dual polyhedron to the small dodecicosidodecahedron is the small dodecacronic hexecontahedron. It is visually identical to the small rhombidodecacron. Its faces are darts. A part of each dart lies inside the solid, hence is invisible in solid models.

Proportions

Faces have two angles of, one of and one of. Its dihedral angles equal. The ratio between the lengths of the long and short edges is.