Small rhombidodecahedron

From HandWiki
Short description: Polyhedron with 42 faces


Small rhombidodecahedron
Small rhombidodecahedron.png
Type Uniform star polyhedron
Elements F = 42, E = 120
V = 60 (χ = −18)
Faces by sides 30{4}+12{10}
Wythoff symbol 2 5 (3/2 5/2) |
Symmetry group Ih, [5,3], *532
Index references U39, C46, W74
Dual polyhedron Small rhombidodecacron
Vertex figure Small rhombidodecahedron vertfig.png
4.10.4/3.10/9
Bowers acronym Sird

File:Small rhombidodecahedron.stl 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.

Related polyhedra

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).

Small rhombicosidodecahedron.png
Rhombicosidodecahedron
Small dodecicosidodecahedron.png
Small dodecicosidodecahedron
Small rhombidodecahedron.png
Small rhombidodecahedron
Small stellated truncated dodecahedron.png
Small stellated truncated dodecahedron
UC36-6 pentagrammic prisms.png
Compound of six pentagrammic prisms
UC37-12 pentagrammic prisms.png
Compound of twelve pentagrammic prisms

Small rhombidodecacron

Small rhombidodecacron
DU39 small rhombidodecacron.png
Type Star polyhedron
Face DU39 facets.png
Elements F = 60, E = 120
V = 42 (χ = −18)
Symmetry group Ih, [5,3], *532
Index references DU39
dual polyhedron Small rhombidodecahedron

File:Small rhombidodecacron.stl 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

External links