Small dodecicosidodecahedron
Encyclopedia
In geometry
, the small dodecicosidodecahedron is a nonconvex uniform polyhedron
, indexed as U33. Its vertex figure
is a crossed quadrilateral.
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
(having the triangular and pentagonal faces in common), and with the small rhombidodecahedron
(having the decagonal 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 dodecicosidodecahedron 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 U33. Its vertex figure
Vertex figure
In geometry a vertex figure is, broadly speaking, the figure exposed when a corner of a polyhedron or polytope is sliced off.-Definitions - theme and variations:...
is a crossed quadrilateral.
Related polyhedra
It shares its vertex arrangementVertex arrangement
In geometry, a vertex arrangement is a set of points in space described by their relative positions. They can be described by their use in polytopes....
with the small stellated truncated dodecahedron and the uniform compounds of 6
Compound of six pentagrammic prisms
This uniform polyhedron compound is a chiral symmetric arrangement of 6 pentagrammic prisms, aligned with the axes of fivefold rotational symmetry of a dodecahedron.- Related polyhedra :...
or 12 pentagrammic prisms
Compound of twelve pentagrammic prisms
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...
. It additionally shares its edge arrangement with the rhombicosidodecahedron
Rhombicosidodecahedron
In geometry, the rhombicosidodecahedron, or small rhombicosidodecahedron, is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces....
(having the triangular and pentagonal faces in common), and with the small rhombidodecahedron
Small rhombidodecahedron
In geometry, the small rhombidodecahedron is a nonconvex uniform polyhedron, indexed as U39. Its vertex figure is a crossed quadrilateral.- Related polyhedra :...
(having the decagonal faces in common).
 Rhombicosidodecahedron Rhombicosidodecahedron In geometry, the rhombicosidodecahedron, or small rhombicosidodecahedron, is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces.... |
 Small dodecicosidodecahedron |
 Small rhombidodecahedron Small rhombidodecahedron In geometry, the small rhombidodecahedron is a nonconvex uniform polyhedron, indexed as U39. Its vertex figure is a crossed quadrilateral.- Related polyhedra :... |
 Small stellated truncated dodecahedron |
 Compound of six pentagrammic prisms Compound of six pentagrammic prisms This uniform polyhedron compound is a chiral symmetric arrangement of 6 pentagrammic prisms, aligned with the axes of fivefold rotational symmetry of a dodecahedron.- Related polyhedra :... |
 Compound of twelve pentagrammic prisms Compound of twelve pentagrammic prisms 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... |