great stellated truncated dodecahedron
{{short description|Polyhedron with 32 faces}}
{{Uniform polyhedra db|Uniform polyhedron stat table|gstD}}
File:Great stellated truncated dodecahedron.stl
In geometry, the great stellated truncated dodecahedron (or quasitruncated great stellated dodecahedron or great stellatruncated dodecahedron) is a nonconvex uniform polyhedron, indexed as U66. It has 32 faces (20 triangles and 12 decagrams), 90 edges, and 60 vertices.{{Cite web|url=https://www.mathconsult.ch/static/unipoly/66.html|title=66: great stellated truncated dodecahedron|last=Maeder|first=Roman|date=|website=MathConsult|archive-url=|archive-date=|access-date=}} It is given a Schläfli symbol {{math|t0,1{5/3,3}.}}
Related polyhedra
It shares its vertex arrangement with three other uniform polyhedra: the small icosicosidodecahedron, the small ditrigonal dodecicosidodecahedron, and the small dodecicosahedron:
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Cartesian coordinates
Cartesian coordinates for the vertices of a great stellated truncated dodecahedron are all the even permutations of
\Bigl(& 0,& \pm\,\varphi,& \pm \bigl[2-\frac{1}{\varphi}\bigr] &\Bigr) \\
\Bigl(& \pm\,\varphi,& \pm\,\frac{1}{\varphi},& \pm\,\frac{2}{\varphi} &\Bigr) \\
\Bigl(& \pm\,\frac{1}{\varphi^2},& \pm\,\frac{1}{\varphi},& \pm\,2 &\Bigr)
\end{array}
where is the golden ratio.
See also
References
{{Reflist}}
External links
- {{mathworld | urlname = GreatStellatedTruncatedDodecahedron| title = Great stellated truncated dodecahedron}}
{{Polyhedron-stub}}