Great truncated icosidodecahedron

In geometry, the great truncated icosidodecahedron (or great quasitruncated icosidodecahedron or stellatruncated icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U68. It has 62 faces (30 squares, 20 hexagons, and 12 decagrams), 180 edges, and 120 vertices.[1] It is given a Schläfli symbol t0,1,2{​5⁄3,3}, and Coxeter-Dynkin diagram, .

Great truncated icosidodecahedron
TypeUniform star polyhedron
ElementsF = 62, E = 180
V = 120 (χ = 2)
Faces by sides30{4}+20{6}+12{10/3}
Wythoff symbol
Symmetry groupIh, [5,3], *532
Index referencesU68, C87, W108
Dual polyhedronGreat disdyakis triacontahedron
Vertex figure
4.6.10/3
Bowers acronymGaquatid
3D model of a great truncated icosidodecahedron

Cartesian coordinates

Cartesian coordinates for the vertices of a great truncated icosidodecahedron centered at the origin are all the even permutations of

(±τ, ±τ, ±(3−1/τ)),
(±2τ, ±1/τ, ±τ−3),
(±τ, ±1/τ2, ±(1+3/τ)),
(±√5, ±2, ±√5/τ) and
(±1/τ, ±3, ±2/τ),

where τ = (1+√5)/2 is the golden ratio.

Great disdyakis triacontahedron
Great disdyakis triacontahedron
TypeStar polyhedron
Face
ElementsF = 120, E = 180
V = 62 (χ = 2)
Symmetry groupIh, [5,3], *532
Index referencesDU68
dual polyhedronGreat truncated icosidodecahedron
3D model of a great disdyakis triacontahedron

The great disdyakis triacontahedron (or trisdyakis icosahedron) is a nonconvex isohedral polyhedron. It is the dual of the great truncated icosidodecahedron. Its faces are triangles.


Proportions

The triangles have one angle of , one of and one of . The dihedral angle equals . Part of each triangle lies within the solid, hence is invisible in solid models.

See also

References
  1. Maeder, Roman. "68: great truncated icosidodecahedron". MathConsult.


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