Great truncated icosidodecahedron
Encyclopedia
In geometry
, the great truncated icosidodecahedron is a nonconvex uniform polyhedron
, indexed as U68. It is given a Schläfli symbol t0,1,2{5/2,3}, and Coxeter-Dynkin diagram
, .
where τ = (1+√5)/2 is the golden ratio
.
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 truncated icosidodecahedron 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 U68. It is given a Schläfli symbol t0,1,2{5/2,3}, and Coxeter-Dynkin diagram
Coxeter-Dynkin diagram
In geometry, a Coxeter–Dynkin diagram is a graph with numerically labeled edges representing the spatial relations between a collection of mirrors...
, .
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, ±(1−2/τ)),
- (±τ, ±1/τ2, ±(1+3/τ)),
- (±(1+2/τ), ±2, ±(2−1/τ)) and
- (±1/τ, ±3, ±2/τ),
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...
.
Trivia
- The name great truncated icosidodecahedron is somewhat misleading: truncation of the pentagrams of a great icosidodecahedron results in pentagons, not decagrams. It's also possible the rectangles will be irregular.