In geometry, the truncated great dodecahedron is a nonconvex uniform polyhedron, indexed as U37. It has 24 faces (12 pentagrams and 12 decagons), 90 edges, and 60 vertices. It is given a Schläfli symbol t{5,5/2}.
Related polyhedra
It shares its vertex arrangement with three other uniform polyhedra: the nonconvex great rhombicosidodecahedron, the great dodecicosidodecahedron, and the great rhombidodecahedron; and with the uniform compounds of 6 or 12 pentagonal prisms.
Nonconvex great rhombicosidodecahedron Great dodecicosidodecahedron Great rhombidodecahedron Truncated great dodecahedron Compound of six pentagonal prisms Compound of twelve pentagonal prisms This polyhedron is the truncation of the great dodecahedron:
The truncated small stellated dodecahedron looks like a dodecahedron on the surface, but it has 24 faces, 12 pentagons from the truncated vertices and 12 overlapping as (truncated pentagrams).
NameSmall stellated dodecahedronTruncated small stellated dodecahedronDodecadodecahedronTruncatedgreatdodecahedronGreatdodecahedronCoxeter-DynkindiagramPicture
Small stellapentakis dodecahedron
The small stellapentakis dodecahedron (or small astropentakis dodecahedron) is a nonconvex isohedral polyhedron. It is the dual of the truncated great dodecahedron. It has 60 intersecting triangular faces.
See also List of uniform polyhedra
References
External links
Uniform polyhedra and duals