The Catalan solid reference article from the English Wikipedia on 24-Jul-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

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 French mathematician, Eugene Catalan who first described them in 1865.

The Catalan solids are all convex. They are face-uniform but not vertex-uniform. This is because the dual Archimedean solids are vertex-uniform and not face uniform. Note that unlike Platonic solids and Archimedean solids, the faces of Catalan solids are not regular polygons. Additionally, two of the Catalan solids are edge-uniform: the rhombic dodecahedron and the rhombic triacontahedron. These are the duals of the two quasi-regular Archimedean solids.

Just like their dual Archimedean partners there are two chiral Catalan solids: the pentagonal icositetrahedron and the pentagonal hexecontahedron. These each come in two enantiomorphs. Not counting the enantimorphs there are a total of 13 Catalan solids.

Name and picture	Dual Archimedean solid	Faces	Edges	Vertices	Face Polygon	Symmetry
rhombic dodecahedron ()	cuboctahedron	12	24	14	rhombus	Oh
rhombic triacontahedron ()	icosidodecahedron	30	60	32	rhombus	Ih
triakis tetrahedron ()	truncated tetrahedron	12	18	8	isosceles triangle	Td
triakis octahedron ()	truncated cube	24	36	14	isosceles triangle	Oh
tetrakis hexahedron ()	truncated octahedron	24	36	14	isosceles triangle	Oh
triakis icosahedron ()	truncated dodecahedron	60	90	32	isosceles triangle	Ih
pentakis dodecahedron ()	truncated icosahedron	60	90	32	isosceles triangle	Ih
deltoidal icositetrahedron ()	rhombicuboctahedron	24	48	26	kite	Oh
disdyakis dodecahedron ()	truncated cuboctahedron	48	72	26	scalene triangle	Oh
deltoidal hexecontahedron ()	rhombicosidodecahedron	60	120	62	kite	Ih
disdyakis triacontahedron ()	truncated icosidodecahedron	120	180	62	scalene triangle	Ih
pentagonal icositetrahedron () ()	snub cube	24	60	38	irregular pentagon	O
pentagonal hexecontahedron () ()	snub dodecahedron	60	150	92	irregular pentagon	I

External links

• Catalan Solid – MathWorld site
• Archimedean duals – at Virtual Reality Polyhedra

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