small dodecahemidodecahedron
{{Short description|Uniform star polyhedron with 18 faces}}
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File:Small dodecahemidodecahedron.stl
In geometry, the small dodecahemidodecahedron is a nonconvex uniform polyhedron, indexed as {{math|U{{sub|51}}}}. It has 18 faces (12 pentagons and 6 decagons), 60 edges, and 30 vertices.{{Cite web|url=https://www.mathconsult.ch/static/unipoly/51.html|title=51: small dodecahemidodecahedron|last=Maeder|first=Roman|date=|website=MathConsult|archive-url=|archive-date=|access-date=}} Its vertex figure alternates two regular pentagons and decagons as a crossed quadrilateral.
It is a hemipolyhedron with six decagonal faces passing through the model center.
Related polyhedra
It shares its edge arrangement with the icosidodecahedron (its convex hull, having the pentagonal faces in common), and with the small icosihemidodecahedron (having the decagonal faces in common).
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References
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External links
- {{mathworld | urlname = SmallDodecahemidodecahedron| title = Small dodecahemidodecahedron}}
- [http://gratrix.net/polyhedra/uniform/summary Uniform polyhedra and duals]
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