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Disdyakis dodecahedron

Disdyakis Dodecahedron

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Disdyakis dodecahedron

A disdyakis dodecahedron, or hexakis octahedron, is a Catalan solid

Catalan solid

In mathematics, a Catalan solid, or Archimedean dual, is a dual polyhedron to an Archimedean solid. The Catalan solids are named for the Belgium mathematician, Eug?ne Catalan, who first described them in 1865....
and the dual to the Archimedean

Archimedean solid

In geometry an Archimedean solid is a highly symmetric, semi-regular convex set polyhedron composed of two or more types of regular polygons meeting in identical vertex ....
truncated cuboctahedron

Truncated cuboctahedron

The truncated cuboctahedron is an Archimedean solid. It has 12 Square faces, 8 regular hexagonal faces, 6 regular octagonal faces, 48 vertices and 72 edges....
. As such it is face-transitive but with irregular face polygons. It looks a bit like an inflated rhombic dodecahedron

Rhombic dodecahedron

The rhombic dodecahedron is a convex set polyhedron with 12 rhombus faces. It is an Archimedean solid solid, or a Catalan solid. Its dual is the cuboctahedron....
— 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.

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Encyclopedia

A disdyakis dodecahedron, or hexakis octahedron, is a Catalan solid

Catalan solid

In mathematics, a Catalan solid, or Archimedean dual, is a dual polyhedron to an Archimedean solid. The Catalan solids are named for the Belgium mathematician, Eug?ne Catalan, who first described them in 1865....
and the dual to the Archimedean

Archimedean solid

In geometry an Archimedean solid is a highly symmetric, semi-regular convex set polyhedron composed of two or more types of regular polygons meeting in identical vertex ....
truncated cuboctahedron

Truncated cuboctahedron

The truncated cuboctahedron is an Archimedean solid. It has 12 Square faces, 8 regular hexagonal faces, 6 regular octagonal faces, 48 vertices and 72 edges....
. As such it is face-transitive but with irregular face polygons. It looks a bit like an inflated rhombic dodecahedron

Rhombic dodecahedron

The rhombic dodecahedron is a convex set polyhedron with 12 rhombus faces. It is an Archimedean solid solid, or a Catalan solid. Its dual is the cuboctahedron....
— 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.

See also

Disdyakis triacontahedron
Disdyakis triacontahedron

A disdyakis triacontahedron, or hexakis icosahedron is a Catalan solid and the dual to the Archimedean solid truncated icosidodecahedron. As such it is face uniform but with irregular face polygons....
Bisected hexagonal tiling

External links

-- Interactive Polyhedron Model