Small stellated truncated dodecahedron
Encyclopedia
In geometry
, the small stellated truncated dodecahedron is a nonconvex uniform polyhedron
, indexed as U58. It is given a Schläfli symbol t0,1{5/3,5}.
It has 12 pentagon
and 12 decagram, {10/3} faces.
with three other uniform polyhedra
: the convex rhombicosidodecahedron
, the small dodecicosidodecahedron
and the small rhombidodecahedron
.
It also has the same vertex arrangement as the uniform compounds
of 6
or 12 pentagrammic prisms
.
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 stellated truncated dodecahedron 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 U58. It is given a Schläfli symbol t0,1{5/3,5}.
It has 12 pentagon
Pentagon
In geometry, a pentagon is any five-sided polygon. A pentagon may be simple or self-intersecting. The sum of the internal angles in a simple pentagon is 540°. A pentagram is an example of a self-intersecting pentagon.- Regular pentagons :In a regular pentagon, all sides are equal in length and...
and 12 decagram, {10/3} faces.
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 three other uniform polyhedra
Uniform polyhedron
A uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive...
: the convex 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....
, the small dodecicosidodecahedron
Small dodecicosidodecahedron
In geometry, the small dodecicosidodecahedron is a nonconvex uniform polyhedron, indexed as U33. Its vertex figure is a crossed quadrilateral.-Related polyhedra:...
and 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 :...
.
It also has the same vertex arrangement as the uniform compounds
Uniform polyhedron compound
A uniform polyhedron compound is a polyhedral compound whose constituents are identical uniform polyhedra, in an arrangement that is also uniform: the symmetry group of the compound acts transitively on the compound's vertices.The uniform polyhedron compounds were first enumerated by John Skilling...
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...
.
 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 dodecicosidodecahedron In geometry, the small dodecicosidodecahedron is a nonconvex uniform polyhedron, indexed as U33. Its vertex figure is a crossed quadrilateral.-Related polyhedra:... |
 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... |