Rhombicosahedron

Rhombicosahedron
Rhombicosahedron.png
Type Uniform star polyhedron
Elements F = 50, E = 120
V = 60 (χ = −10)
Faces by sides 30{4}+20{6}
Wythoff symbol 2 3 (5/4 5/2) |
Symmetry group Ih, [5,3], *532
Index references U56, C72, W96
Dual polyhedron Rhombicosacron
Vertex figure Rhombicosahedron vertfig.png
4.6.4/3.6/5
Bowers acronym Ri

In geometry, the rhombicosahedron is a nonconvex uniform polyhedron, indexed as U56. It has 50 faces (30 squares and 20 hexagons), 120 edges and 60 vertices.[1] Its vertex figure is an antiparallelogram.

3D model of a rhombicosahedron

Related polyhedraEdit

A rhombicosahedron shares its vertex arrangement with the uniform compounds of 10 or 20 triangular prisms. It additionally shares its edges with the rhombidodecadodecahedron (having the square faces in common) and the icosidodecadodecahedron (having the hexagonal faces in common).

 
Convex hull
 
Rhombidodecadodecahedron
 
Icosidodecadodecahedron
 
Rhombicosahedron
 
Compound of ten triangular prisms
 
Compound of twenty triangular prisms


RhombicosacronEdit

Rhombicosacron
 
Type Star polyhedron
Face  
Elements F = 60, E = 120
V = 50 (χ = −10)
Symmetry group Ih, [5,3], *532
Index references DU56
dual polyhedron Rhombicosahedron
 
3D model of a rhombicosacron

The rhombicosacron is a nonconvex isohedral polyhedron. It is the dual of the uniform rhombicosahedron, U56. It has 50 vertices, 120 edges, and 60 crossed-quadrilateral faces.

ReferencesEdit

  1. ^ Maeder, Roman. "56: rhombicosahedron". MathConsult.

External linksEdit