Icositruncated dodecadodecahedron
Encyclopedia
In geometry
, the icositruncated dodecadodecahedron is a nonconvex uniform polyhedron
, indexed as U45.
is a nonuniform great rhombicosidodecahedron.
where τ = (1+√5)/2 is the golden ratio
(sometimes written φ).
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, the icositruncated dodecadodecahedron is a nonconvex uniform polyhedron
Nonconvex uniform polyhedron
In geometry, a uniform star polyhedron is a self-intersecting uniform polyhedron. They are also sometimes called nonconvex polyhedra to imply self-intersecting...
, indexed as U45.
Convex hull
Its convex hullConvex hull
In mathematics, the convex hull or convex envelope for a set of points X in a real vector space V is the minimal convex set containing X....
is a nonuniform great rhombicosidodecahedron.
 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
Golden ratio
In mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The golden ratio is an irrational mathematical constant, approximately 1.61803398874989...
(sometimes written φ).