Icositruncated dodecadodecahedron

Icositruncated dodecadodecahedron
TypeUniform star polyhedron
ElementsF = 44, E = 180
V = 120 (χ = 16)
Faces by sides20{6}+12{10}+12{10/3}
Wythoff symbol3 5 5/3 |
Symmetry groupIh, [5,3], *532
Index referencesU45, C57, W84
Dual polyhedronTridyakis icosahedron
Vertex figure
6.10.10/3
Bowers acronymIdtid

In geometry, the icositruncated dodecadodecahedron or icosidodecatruncated icosidodecahedron is a nonconvex uniform polyhedron, indexed as U45.

Convex hull

Its convex hull is a nonuniform truncated icosidodecahedron.


truncated icosidodecahedron

Convex hull

Icositruncated dodecadodecahedron

Cartesian coordinates

Cartesian coordinates for the vertices of an icositruncated dodecadodecahedron are all the even permutations of

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

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


Related polyhedra

Tridyakis icosahedron

Tridyakis icosahedron
TypeStar polyhedron
Face
ElementsF = 120, E = 180
V = 44 (χ = 16)
Symmetry groupIh, [5,3], *532
Index referencesDU45
dual polyhedronIcositruncated dodecadodecahedron

The tridyakis icosahedron is the dual polyhedron of the nonconvex uniform polyhedron, icositruncated dodecadodecahedron. It has 44 vertices, 180 edges, and 120 scalene triangular faces.

See also

References

External links