Small icosicosidodecahedron
Encyclopedia
In geometry
, the small icosicosidodecahedron is a nonconvex uniform polyhedron
, indexed as U31.
(having the triangular and pentagrammic faces in common) and the small dodecicosahedron
(having the hexagonal faces in common).
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, the small icosicosidodecahedron is a nonconvex uniform polyhedron
Nonconvex uniform polyhedron
In geometry, a uniform star polyhedron is a self-intersecting uniform polyhedron. They are also sometimes called nonconvex polyhedra to imply self-intersecting...
, indexed as U31.
Related polyhedra
It shares its vertex arrangement with the great stellated truncated dodecahedron. It additionally shares its edges with the small ditrigonal dodecicosidodecahedronSmall ditrigonal dodecicosidodecahedron
In geometry, the small ditrigonal dodecicosidodecahedron is a nonconvex uniform polyhedron, indexed as U43. Its vertex figure is a crossed quadrilateral.- Related polyhedra :It shares its vertex arrangement with the great stellated truncated dodecahedron...
(having the triangular and pentagrammic faces in common) and the small dodecicosahedron
Small dodecicosahedron
In geometry, the small dodecicosahedron is a nonconvex uniform polyhedron, indexed as U50. Its vertex figure is a crossed quadrilateral.-Related polyhedra:It shares its vertex arrangement with the great stellated truncated dodecahedron...
(having the hexagonal faces in common).
 Great stellated truncated dodecahedron |
 Small icosicosidodecahedron |
 Small ditrigonal dodecicosidodecahedron Small ditrigonal dodecicosidodecahedron In geometry, the small ditrigonal dodecicosidodecahedron is a nonconvex uniform polyhedron, indexed as U43. Its vertex figure is a crossed quadrilateral.- Related polyhedra :It shares its vertex arrangement with the great stellated truncated dodecahedron... |
 Small dodecicosahedron Small dodecicosahedron In geometry, the small dodecicosahedron is a nonconvex uniform polyhedron, indexed as U50. Its vertex figure is a crossed quadrilateral.-Related polyhedra:It shares its vertex arrangement with the great stellated truncated dodecahedron... |