Rhombicosahedron
Encyclopedia
In geometry
, the rhombicosahedron is a nonconvex uniform polyhedron
, indexed as U56. Its vertex figure
is an antiparallelogram
.
with the uniform compounds of 10
or 20 triangular prisms
. It additionally shares its edges with the rhombidodecadodecahedron (having the square faces in common) and the icosidodecadodecahedron
(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 rhombicosahedron 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 U56. 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 an antiparallelogram
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
A rhombicosahedron 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 uniform compounds of 10
Compound of ten triangular prisms
This uniform polyhedron compound is a chiral symmetric arrangement of 10 triangular prisms, aligned with the axes of three-fold rotational symmetry of an icosahedron.- Relatde polyhedra :...
or 20 triangular prisms
Compound of twenty triangular prisms
This uniform polyhedron compound is a symmetric arrangement of 20 triangular prisms, aligned in pairs with the axes of three-fold rotational symmetry of an icosahedron.It results from composing the two enantiomorphs of the compound of 10 triangular prisms...
. It additionally shares its edges with the rhombidodecadodecahedron (having the square faces in common) and the icosidodecadodecahedron
Icosidodecadodecahedron
In geometry, the icosidodecadodecahedron is a nonconvex uniform polyhedron, indexed as U44. Its vertex figure is a crossed quadrilateral.- Related polyhedra :It shares its vertex arrangement with the uniform compounds of 10 or 20 triangular prisms...
(having the hexagonal faces in common).
 convex hull Convex hull In mathematics, the convex hull or convex envelope for a set of points X in a real vector space V is the minimal convex set containing X.... |
 Rhombidodecadodecahedron |
 Icosidodecadodecahedron Icosidodecadodecahedron In geometry, the icosidodecadodecahedron is a nonconvex uniform polyhedron, indexed as U44. Its vertex figure is a crossed quadrilateral.- Related polyhedra :It shares its vertex arrangement with the uniform compounds of 10 or 20 triangular prisms... |
 Rhombicosahedron |
 Compound of ten triangular prisms Compound of ten triangular prisms This uniform polyhedron compound is a chiral symmetric arrangement of 10 triangular prisms, aligned with the axes of three-fold rotational symmetry of an icosahedron.- Relatde polyhedra :... |
 Compound of twenty triangular prisms Compound of twenty triangular prisms This uniform polyhedron compound is a symmetric arrangement of 20 triangular prisms, aligned in pairs with the axes of three-fold rotational symmetry of an icosahedron.It results from composing the two enantiomorphs of the compound of 10 triangular prisms... |