Great stellated truncated dodecahedron

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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. It is given a Schläfli symbol Template:Math

Related polyhedra

It shares its vertex arrangement with three other uniform polyhedra: the small icosicosidodecahedron, the small ditrigonal dodecicosidodecahedron, and the small dodecicosahedron:

Great stellated truncated dodecahedron

Small icosicosidodecahedron

Small ditrigonal dodecicosidodecahedron

Small dodecicosahedron

Cartesian coordinates

Cartesian coordinates for the vertices of a great stellated truncated dodecahedron are all the even permutations of $$\begin{array}{ccccc}(& 0,& \pm \phi ,& \pm [2-\frac{1}{\phi }]& )\\ (& \pm \phi ,& \pm \frac{1}{\phi },& \pm \frac{2}{\phi }& )\\ (& \pm \frac{1}{{\phi }^2},& \pm \frac{1}{\phi },& \pm 2& )\end{array}$$

where $\phi =\frac{1+\sqrt{5}}{2}$ is the golden ratio.

See also

• List of uniform polyhedra

External links

• Template:Mathworld

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