Great ditrigonal icosidodecahedron
Encyclopedia
In geometry
, the great ditrigonal icosidodecahedron is a nonconvex uniform polyhedron
, indexed as U47.
Its circumradius is
times the length of its edge, a value it shares with the cube
.
is a regular dodecahedron. It additionally shares its edge arrangement with the small ditrigonal icosidodecahedron
(having the triangular faces in common), the ditrigonal dodecadodecahedron
(having the pentagonal faces in common), and the regular compound of five cubes
.
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 ditrigonal icosidodecahedron 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 U47.
Its circumradius is
times the length of its edge, a value it shares with the cubeCube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube can also be called a regular hexahedron and is one of the five Platonic solids. It is a special kind of square prism, of rectangular parallelepiped and...
.
Related polyhedra
Its convex hullConvex 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....
is a regular dodecahedron. It additionally shares its edge arrangement with the small ditrigonal icosidodecahedron
Small ditrigonal icosidodecahedron
In geometry, the small ditrigonal icosidodecahedron is a nonconvex uniform polyhedron, indexed as U30.-Related polyhedra:Its convex hull is a regular dodecahedron...
(having the triangular faces in common), the ditrigonal dodecadodecahedron
Ditrigonal dodecadodecahedron
In geometry, the Ditrigonal dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U41.- Related polyhedra :Its convex hull is a regular dodecahedron...
(having the pentagonal faces in common), and the regular compound of five cubes
Compound of five cubes
This polyhedral compound is a symmetric arrangement of five cubes. This compound was first described by Edmund Hess in 1876.It is one of five regular compounds, and dual to the compound of five octahedra....
.
 Small ditrigonal icosidodecahedron Small ditrigonal icosidodecahedron In geometry, the small ditrigonal icosidodecahedron is a nonconvex uniform polyhedron, indexed as U30.-Related polyhedra:Its convex hull is a regular dodecahedron... |
 Great ditrigonal icosidodecahedron |
 Ditrigonal dodecadodecahedron Ditrigonal dodecadodecahedron In geometry, the Ditrigonal dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U41.- Related polyhedra :Its convex hull is a regular dodecahedron... |
 Dodecahedron (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.... ) |
 Compound of five cubes Compound of five cubes This polyhedral compound is a symmetric arrangement of five cubes. This compound was first described by Edmund Hess in 1876.It is one of five regular compounds, and dual to the compound of five octahedra.... |
External links
- VRMLVRMLVRML is a standard file format for representing 3-dimensional interactive vector graphics, designed particularly with the World Wide Web in mind...
model: http://www.physics.orst.edu/~bulatov/polyhedra/uniform/u52.html - MathWorld