Great ditrigonal icosidodecahedron

Great ditrigonal icosidodecahedron
Great ditrigonal icosidodecahedron.png
Type Uniform star polyhedron
Elements F = 32, E = 60
V = 20 (χ = −8)
Faces by sides 20{3}+12{5}
Wythoff symbol 3/2 | 3 5
3 | 3/2 5
3 | 3 5/4
3/2 | 3/2 5/4
Symmetry group Ih, [5,3], *532
Index references U47, C61, W87
Dual polyhedron Great triambic icosahedron
Vertex figure Great ditrigonal icosidodecahedron vertfig.png
((3.5)3)/2
Bowers acronym Gidtid

In geometry, the great ditrigonal icosidodecahedron (or great ditrigonary icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U47. It has 32 faces (20 triangles and 12 pentagrams), 60 edges, and 20 vertices.[1] It has 4 Schwarz triangle equivalent constructions, for example Wythoff symbol 3 | 3 ​54 gives Coxeter diagram CDel label5-4.pngCDel branch 10ru.pngCDel split2.pngCDel node.png = CDel node h3.pngCDel 5-2.pngCDel node.pngCDel 3.pngCDel node.png. It has extended Schläfli symbol a{​52,3} or c{3,​52}, as an altered great stellated dodecahedron or converted great icosahedron.

3D model of a great ditrigonal icosidodecahedron

Its circumradius is ​32 times the length of its edge,[2] a value it shares with the cube.

Related polyhedraEdit

Its convex hull is a regular dodecahedron. It additionally shares its edge arrangement with the small ditrigonal icosidodecahedron (having the triangular faces in common), the ditrigonal dodecadodecahedron (having the pentagonal faces in common), and the regular compound of five cubes.

a{5,3} a{5/2,3} b{5,5/2}
     =            =            
 
Small ditrigonal icosidodecahedron
 
Great ditrigonal icosidodecahedron
 
Ditrigonal dodecadodecahedron
 
Dodecahedron (convex hull)
 
Compound of five cubes

ReferencesEdit

  1. ^ Maeder, Roman. "47: great ditrigonal icosidodecahedron". MathConsult.
  2. ^ Weisstein, Eric W (2003), CRC concise encyclopedia of mathematics, Boca Raton: Chapman & Hall/CRC, ISBN 1-58488-347-2

External linksEdit