Great stellated truncated dodecahedron

Great stellated truncated dodecahedron
File:Great stellated truncated dodecahedron.png
Type	Uniform star polyhedron
Elements	F = 32, E = 90 V = 60 (χ = 2)
Faces by sides	20{3}+12{10/3}
Coxeter diagram	Template:CDD
Wythoff symbol	5/3
Symmetry group	Ih, [5,3], *532
Index references	U66, C83, W104
Dual polyhedron	Great triakis icosahedron
Vertex figure	File:Great stellated truncated dodecahedron vertfig.png 3.10/3.10/3
Bowers acronym	Quit Gissid

File:Great stellated truncated dodecahedron.stl

3D model of a great stellated truncated dodecahedron

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:

File:Great stellated truncated dodecahedron.png Great stellated truncated dodecahedron

File:Small icosicosidodecahedron.png Small icosicosidodecahedron

File:Small ditrigonal dodecicosidodecahedron.png Small ditrigonal dodecicosidodecahedron

File:Small dodecicosahedron.png Small dodecicosahedron

Cartesian coordinates

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

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

See also

• List of uniform polyhedra

External links

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