Great stellated truncated dodecahedron
Encyclopedia
In geometry
, the great stellated truncated dodecahedron is a nonconvex uniform polyhedron
, indexed as U66. It is given a Schläfli symbol t0,1{5/3,3}.
with three other uniform polyhedra
: the small icosicosidodecahedron
, the small ditrigonal dodecicosidodecahedron
, and the small dodecicosahedron
:
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 great stellated truncated dodecahedron 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 U66. It is given a Schläfli symbol t0,1{5/3,3}.
Related polyhedra
It shares its vertex arrangementVertex arrangement
In geometry, a vertex arrangement is a set of points in space described by their relative positions. They can be described by their use in polytopes....
with three other uniform polyhedra
Uniform polyhedron
A uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive...
: the small icosicosidodecahedron
Small icosicosidodecahedron
In geometry, the small icosicosidodecahedron is a nonconvex uniform polyhedron, indexed as U31.- Related polyhedra :It shares its vertex arrangement with the great stellated truncated dodecahedron...
, the small ditrigonal dodecicosidodecahedron
Small ditrigonal dodecicosidodecahedron
In geometry, the small ditrigonal dodecicosidodecahedron is a nonconvex uniform polyhedron, indexed as U43. Its vertex figure is a crossed quadrilateral.- Related polyhedra :It shares its vertex arrangement with the great stellated truncated dodecahedron...
, and the small dodecicosahedron
Small dodecicosahedron
In geometry, the small dodecicosahedron is a nonconvex uniform polyhedron, indexed as U50. Its vertex figure is a crossed quadrilateral.-Related polyhedra:It shares its vertex arrangement with the great stellated truncated dodecahedron...
:
 Great stellated truncated dodecahedron |
 Small icosicosidodecahedron Small icosicosidodecahedron In geometry, the small icosicosidodecahedron is a nonconvex uniform polyhedron, indexed as U31.- Related polyhedra :It shares its vertex arrangement with the great stellated truncated dodecahedron... |
 Small ditrigonal dodecicosidodecahedron Small ditrigonal dodecicosidodecahedron In geometry, the small ditrigonal dodecicosidodecahedron is a nonconvex uniform polyhedron, indexed as U43. Its vertex figure is a crossed quadrilateral.- Related polyhedra :It shares its vertex arrangement with the great stellated truncated dodecahedron... |
 Small dodecicosahedron Small dodecicosahedron In geometry, the small dodecicosahedron is a nonconvex uniform polyhedron, indexed as U50. Its vertex figure is a crossed quadrilateral.-Related polyhedra:It shares its vertex arrangement with the great stellated truncated dodecahedron... |
Cartesian coordinates
Cartesian coordinates for the vertices of a great stellated truncated dodecahedron are all the even permutations of- (0, ±τ, ±(2−1/τ))
- (±τ, ±1/τ, ±2/τ)
- (±1/τ2, ±1/τ, ±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).