Small rhombidodecahedron
{{Short description|Polyhedron with 42 faces}}
{{Uniform polyhedra db|Uniform polyhedron stat table|lrD}}
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.{{Cite web|url=https://www.mathconsult.ch/static/unipoly/39.html|title=39: small rhombidodecahedron|last=Maeder|first=Roman|date=|website=MathConsult|archive-url=|archive-date=|access-date=}} 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).
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= Small rhombidodecacron=
{{Uniform polyhedra db|Uniform dual polyhedron stat table|lrD}}
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
{{Reflist}}
- {{Citation | last1=Wenninger | first1=Magnus | author1-link=Magnus Wenninger | title=Dual Models | publisher=Cambridge University Press | isbn=978-0-521-54325-5 |mr=730208 | year=1983}}
External links
- {{mathworld | urlname = SmallRhombidodecahedron| title = Small rhombidodecahedron}}
- {{mathworld | urlname = SmallRhombidodecacron| title =Small rhombidodecacron}}
- [http://gratrix.net/polyhedra/uniform/summary Uniform polyhedra and duals]
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