great dodecahemidodecahedron
{{Short description|Polyhedron with 18 faces}}
{{Uniform polyhedra db|Uniform polyhedron stat table|gDhD}}
File:Great dodecahemidodecahedron.stl
In geometry, the great dodecahemidodecahedron is a nonconvex uniform polyhedron, indexed as U70. It has 18 faces (12 pentagrams and 6 decagrams), 60 edges, and 30 vertices.{{Cite web|url=https://www.mathconsult.ch/static/unipoly/70.html|title=70: great dodecahemidodecahedron|last=Maeder|first=Roman|date=|website=MathConsult|archive-url=|archive-date=|access-date=}} Its vertex figure is a crossed quadrilateral.
Aside from the regular small stellated dodecahedron {5/2,5} and great stellated dodecahedron {5/2,3}, it is the only nonconvex uniform polyhedron whose faces are all non-convex regular polygons (star polygons), namely the star polygons {5/2} and {10/3}.
It is a hemipolyhedron with 6 decagrammic faces passing through the model center.
Related polyhedra
Its convex hull is the icosidodecahedron. It also shares its edge arrangement with the great icosidodecahedron (having the pentagrammic faces in common) and the great icosihemidodecahedron (having the decagrammic faces in common).
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| align=center|100px Icosidodecahedron (convex hull) |
Gallery
See also
References
{{reflist}}
External links
- {{mathworld | urlname = GreatDodecahemidodecahedron| title = Great dodecahemidodecahedron}}
- [http://gratrix.net/polyhedra/uniform/summary Uniform polyhedra and duals]
{{Nonconvex polyhedron navigator}}