Concept
Great icosicosidodecahedron
Related concepts (4)
Great ditrigonal dodecicosidodecahedron
In geometry, the great ditrigonal dodecicosidodecahedron (or great dodekified icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U42. It has 44 faces (20 triangles, 12 pentagons, and 12 decagrams), 120 edges, and 60 vertices. Its vertex figure is an isosceles trapezoid. It shares its vertex arrangement with the truncated dodecahedron. It additionally shares its edge arrangement with the great icosicosidodecahedron (having the triangular and pentagonal faces in common) and the great dodecicosahedron (having the decagrammic faces in common).
Great dodecicosahedron
In geometry, the great dodecicosahedron (or great dodekicosahedron) is a nonconvex uniform polyhedron, indexed as U63. It has 32 faces (20 hexagons and 12 decagrams), 120 edges, and 60 vertices. Its vertex figure is a crossed quadrilateral. It has a composite Wythoff symbol, 3 ( ) |, requiring two different Schwarz triangles to generate it: (3 ) and (3 ). (3 | represents the great dodecicosahedron with an extra 12 pentagons, and 3 | represents it with an extra 20 triangles.) Its vertex figure 6...
Uniform star polyhedron
In geometry, a uniform star polyhedron is a self-intersecting uniform polyhedron. They are also sometimes called nonconvex polyhedra to imply self-intersecting. Each polyhedron can contain either star polygon faces, star polygon vertex figures, or both. The complete set of 57 nonprismatic uniform star polyhedra includes the 4 regular ones, called the Kepler–Poinsot polyhedra, 5 quasiregular ones, and 48 semiregular ones. There are also two infinite sets of uniform star prisms and uniform star antiprisms.
Truncated dodecahedron
In geometry, the truncated dodecahedron is an Archimedean solid. It has 12 regular decagonal faces, 20 regular triangular faces, 60 vertices and 90 edges. This polyhedron can be formed from a regular dodecahedron by truncating (cutting off) the corners so the pentagon faces become decagons and the corners become triangles. It is used in the cell-transitive hyperbolic space-filling tessellation, the bitruncated icosahedral honeycomb.