Great rhombidodecahedron
Encyclopedia
In geometry
, the great rhombidodecahedron is a nonconvex uniform polyhedron
, indexed as U73. Its vertex figure
is a crossed quadrilateral
.
with the truncated great dodecahedron and the uniform compounds of 6
or 12 pentagonal prisms
. It additionally shares its edge arrangement with the nonconvex great rhombicosidodecahedron (having the square faces in common), and with the great dodecicosidodecahedron
(having the decagrammic 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 great rhombidodecahedron 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 U73. 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
Antiparallelogram
An antiparallelogram is a quadrilateral in which, like a parallelogram, the pairs of nonadjacent sides are congruent, but in which two opposite sides intersect and are therefore not parallel.-Properties:Every antiparallelogram has an axis of symmetry through its crossing point...
.
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 truncated great dodecahedron and the uniform compounds of 6
Compound of six pentagonal prisms
This uniform polyhedron compound is a chiral symmetric arrangement of 6 pentagonal prisms, aligned with the axes of fivefold rotational symmetry of a dodecahedron.- Related polyhedra :...
or 12 pentagonal prisms
Compound of twelve pentagonal prisms
This uniform polyhedron compound is a symmetric arrangement of 12 pentagonal 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 pentagonal prisms...
. It additionally shares its edge arrangement with the nonconvex great rhombicosidodecahedron (having the square faces in common), and with the great dodecicosidodecahedron
Great dodecicosidodecahedron
In geometry, the great dodecicosidodecahedron is a nonconvex uniform polyhedron, indexed as U61.- Related polyhedra :It shares its vertex arrangement with the truncated great dodecahedron and the uniform compounds of 6 or 12 pentagonal prisms...
(having the decagrammic faces in common).
 Nonconvex great rhombicosidodecahedron |
 Great dodecicosidodecahedron Great dodecicosidodecahedron In geometry, the great dodecicosidodecahedron is a nonconvex uniform polyhedron, indexed as U61.- Related polyhedra :It shares its vertex arrangement with the truncated great dodecahedron and the uniform compounds of 6 or 12 pentagonal prisms... |
 Great rhombidodecahedron |
 Truncated great dodecahedron |
 Compound of six pentagonal prisms Compound of six pentagonal prisms This uniform polyhedron compound is a chiral symmetric arrangement of 6 pentagonal prisms, aligned with the axes of fivefold rotational symmetry of a dodecahedron.- Related polyhedra :... |
 Compound of twelve pentagonal prisms Compound of twelve pentagonal prisms This uniform polyhedron compound is a symmetric arrangement of 12 pentagonal 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 pentagonal prisms... |