Catalan solid

The Catalan Solid for scale, by midradius

A Catalan solid is convex isohedral polyhedron with a single dihedral angle, other than the regular polyhedra and the infinite families of bipyramids and trapezohedra. They Catalan solids are the duals of the Archimedean solids. There are thirteen Catalan solids.

They were described by a Belgian mathematician Eugène Catalan in 1865.

List of the Catalan solids[edit | edit source]

Name	Faces	Edges	Vertices	Dual
Triakis tetrahedron	12 isosceles triangles	6+12	4+4	Truncated tetrahedron
Rhombic dodecahedron	12 rhombi	24	6+8	Cuboctahedron
Triakis octahedron	24 isosceles triangles	12+24	6+8	Truncated cube
Tetrakis hexahedron	24 isosceles triangles	12+24	6+8	Truncated octahedron
Deltoidal icositetrahedron	24 isosceles trapezoids	24+24	6+8+12	Small rhombicuboctahedron
Pentagonal icositetrahedron	24 floret pentagons	12+24+24	6+8+24	Snub cube
Disdyakis dodecahedron	48 scalene triangles	24+24+24	6+8+12	Great rhombicuboctahedron
Rhombic triacontahedron	30 rhombi	60	12+20	Icosidodecahedron
Triakis icosahedron	60 isosceles triangles	30+60	12+20	Truncated dodecahedron
Pentakis dodecahedron	60 isosceles triangles	30+60	12+20	Truncated icosahedron
Deltoidal hexecontahedron	60 isosceles trapezoids	60+60	12+20+30	Small rhombicosidodecahedron
Pentagonal hexecontahedron	60 floret pentagons	30+60+60	12+20+60	Snub dodecahedron
Disdyakis triacontahedron	120 scalene triangles	60+60+60	12+20+30	Great rhombicosidodecahedron