Tridyakis icosahedron
Encyclopedia
In geometry
, 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.
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 tridyakis icosahedron is the dual polyhedron
Dual polyhedron
In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other. The dual of the dual is the original polyhedron. The dual of a polyhedron with equivalent vertices is one with equivalent faces, and of one with equivalent edges is another...
of the nonconvex uniform polyhedron
Star polyhedron
In geometry, a star polyhedron is a polyhedron which has some repetitive quality of nonconvexity giving it a star-like visual quality.There are two general kinds of star polyhedron:*Polyhedra which self-intersect in a repetitive way....
, icositruncated dodecadodecahedron
Icositruncated dodecadodecahedron
In geometry, the icositruncated dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U45.- Convex hull :Its convex hull is a nonuniform great rhombicosidodecahedron.- Cartesian coordinates :...
. It has 44 vertices, 180 edges, and 120 scalene triangular faces.
See also
- Catalan solidCatalan solidIn mathematics, a Catalan solid, or Archimedean dual, is a dual polyhedron to an Archimedean solid. The Catalan solids are named for the Belgian mathematician, Eugène Catalan, who first described them in 1865....
Duals to convex uniform polyhedra - Uniform polyhedra
- List of uniform polyhedra