In geometry, the small dodecicosidodecahedron (or small dodekicosidodecahedron) is a nonconvex uniform polyhedron, indexed as U33. It has 44 faces (20 triangles, 12 pentagons, and 12 decagons), 120 edges, and 60 vertices.[1] Its vertex figure is a crossed quadrilateral.
Small dodecicosidodecahedron | |
---|---|
Type | Uniform star polyhedron |
Elements | F = 44, E = 120 V = 60 (χ = −16) |
Faces by sides | 20{3}+12{5}+12{10} |
Coxeter diagram | |
Wythoff symbol | 3/2 5 | 5 3 5/4 | 5 |
Symmetry group | Ih, [5,3], *532 |
Index references | U33, C42, W72 |
Dual polyhedron | Small dodecacronic hexecontahedron |
Vertex figure | 5.10.3/2.10 |
Bowers acronym | Saddid |
Related polyhedra
It shares its vertex arrangement with the small stellated truncated dodecahedron and the uniform compounds of 6 or 12 pentagrammic prisms. It additionally shares its edge arrangement with the rhombicosidodecahedron (having the triangular and pentagonal faces in common), and with the small rhombidodecahedron (having the decagonal faces in common).
Rhombicosidodecahedron |
Small dodecicosidodecahedron |
Small rhombidodecahedron |
Small stellated truncated dodecahedron |
Compound of six pentagrammic prisms |
Compound of twelve pentagrammic prisms |
Dual
Small dodecacronic hexecontahedron | |
---|---|
Type | Star polyhedron |
Face | |
Elements | F = 60, E = 120 V = 44 (χ = −16) |
Symmetry group | Ih, [5,3], *532 |
Index references | DU33 |
dual polyhedron | Small dodecicosidodecahedron |
The dual polyhedron to the small dodecicosidodecahedron is the small dodecacronic hexecontahedron (or small sagittal ditriacontahedron). It is visually identical to the small rhombidodecacron. Its faces are darts. A part of each dart lies inside the solid, hence is invisible in solid models.
Proportions
Faces have two angles of , one of and one of . Its dihedral angles equal . The ratio between the lengths of the long and short edges is .
References
External links
Wikiwand in your browser!
Seamless Wikipedia browsing. On steroids.
Every time you click a link to Wikipedia, Wiktionary or Wikiquote in your browser's search results, it will show the modern Wikiwand interface.
Wikiwand extension is a five stars, simple, with minimum permission required to keep your browsing private, safe and transparent.