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}
Wythoff symbol
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.


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