Small rhombidodecahedron

In geometry, the small rhombidodecahedron is a nonconvex uniform polyhedron, indexed as U39. It has 42 faces (30 squares and 12 decagons), 120 edges, and 60 vertices.[1] Its vertex figure is a crossed quadrilateral.

Small rhombidodecahedron
TypeUniform star polyhedron
ElementsF = 42, E = 120
V = 60 (χ = −18)
Faces by sides30{4}+12{10}
Coxeter diagram (with extra double-covered triangles)
(with extra double-covered pentagons)
Wythoff symbol2 5 (3/2 5/2) |
Symmetry groupIh, [5,3], *532
Index referencesU39, C46, W74
Dual polyhedronSmall rhombidodecacron
Vertex figure
4.10.4/3.10/9
Bowers acronymSird
3D model of a small rhombidodecahedron

It shares its vertex arrangement with the small stellated truncated dodecahedron and the uniform compounds of 6 or 12 pentagrammic prisms. It additionally shares its edge arrangement with the rhombicosidodecahedron (having the square faces in common), and with the small dodecicosidodecahedron (having the decagonal faces in common).


Rhombicosidodecahedron
Small dodecicosidodecahedron
Small rhombidodecahedron

Small stellated truncated dodecahedron
Compound of six pentagrammic prisms
Compound of twelve pentagrammic prisms

Small rhombidodecacron
Small rhombidodecacron
TypeStar polyhedron
Face
ElementsF = 60, E = 120
V = 42 (χ = −18)
Symmetry groupIh, [5,3], *532
Index referencesDU39
dual polyhedronSmall rhombidodecahedron
3D model of a small rhombidodecacron

The small rhombidodecacron (or small dipteral ditriacontahedron) is a nonconvex isohedral polyhedron. It is the dual of the small rhombidodecahedron. It is visually identical to the Small dodecacronic hexecontahedron. It has 60 intersecting antiparallelogram faces.

References
  1. Maeder, Roman. "39: small rhombidodecahedron". MathConsult.{{cite web}}: CS1 maint: url-status (link)


This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.