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Encyclopedia > Disdyakis dodecahedron
Disdyakis dodecahedron Click on picture for large version.
Type Catalan
Face polygon scalene triangle
Faces 48
Edges 72
Vertices 26 = 6 + 8 + 12
Face configuration 4,6,8
Symmetry group octahedral (Oh)
Dual polyhedron truncated cuboctahedron
Properties convex, face-uniform

A disdyakis dodecahedron, or hexakis octahedron, is the Catalan solid whose Archimedean dual is the truncated cuboctahedron. As such it is face uniform but with irregular face polygons. It looks a bit like an inflated rhombic dodecahedron — if one replaces each face of the rhombic dodecahedron with a single vertex and four triangles in a regular fashion one ends up with a disdyakis dodecahedron. Download high resolution version (765x802, 94 KB)Disdyakis dodecahedron, made by me using POV-Ray, see image:poly. ... Spinning disdyakis dodecahedron, made by me using POV-Ray, see image:poly. ... A rhombic dodecahedron In mathematics, a Catalan solid, or Archimedean dual, is a dual polyhedron to an Archimedean solid. ... For alternate meanings, such as the musical instrument, see triangle (disambiguation). ... The symmetry group of an object (e. ... In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other. ... The truncated cuboctahedron, or great rhombicuboctahedron, is an Archimedean solid. ... A rhombic dodecahedron In mathematics, a Catalan solid, or Archimedean dual, is a dual polyhedron to an Archimedean solid. ... In geometry an Archimedean solid or semi-regular solid is a semi-regular convex polyhedron composed of two or more types of regular polygon meeting in identical vertices. ... The truncated cuboctahedron, or great rhombicuboctahedron, is an Archimedean solid. ... The rhombic dodecahedron is a convex polyhedron with 12 rhombic faces. ...

A disdyakis triacontahedron, or hexakis icosahedron is the Catalan solid whose Archimedean dual is the truncated icosidodecahedron. ... Results from FactBites:

 rhombic dodecahedron: Information From Answers.com (233 words) Being the dual of an Archimedean polyhedron, the rhombic dodecahedron is face-uniform, meaning the symmetry group of the solid acts transitively on the set of faces. Honeybees use the geometry of rhombic dodecahedra to form honeycomb from a tessellation of cells each of which is a hexagonal prism capped with half a rhombic dodecahedron. The rhombic dodecahedron forms the (hull of the) projection of a tesseract to 3 dimensions.
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