Ditrigonal dodecadodecahedron

Ditrigonal dodecadodecahedron
Ditrigonal dodecadodecahedron.png
Type Uniform star polyhedron
Elements F = 24, E = 60
V = 20 (χ = −16)
Faces by sides 12{5}+12{5/2}
Wythoff symbol 3 | 5/3 5
3/2 | 5 5/2
3/2 | 5/3 5/4
3 | 5/2 5/4
Symmetry group Ih, [5,3], *532
Index references U41, C53, W80
Dual polyhedron Medial triambic icosahedron
Vertex figure Ditrigonal dodecadodecahedron vertfig.png
Bowers acronym Ditdid
3D model of a ditrigonal dodecadodecahedron

In geometry, the ditrigonal dodecadodecahedron (or ditrigonary dodecadodecahedron) is a nonconvex uniform polyhedron, indexed as U41. It has 24 faces (12 pentagons and 12 pentagrams), 60 edges, and 20 vertices.[1] It has extended Schläfli symbol b{5,​52}, as a blended great dodecahedron, and Coxeter diagram CDel node.pngCDel 5.pngCDel node h3.pngCDel 5-2.pngCDel node.png. It has 4 Schwarz triangle equivalent constructions, for example Wythoff symbol 3 | ​53 5, and Coxeter diagram Ditrigonal dodecadodecahedron cd.png.

Related polyhedraEdit

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

a{5,3} a{​52,3} b{5,​52}
     =            =         =      
Small ditrigonal icosidodecahedron
Great ditrigonal icosidodecahedron
Ditrigonal dodecadodecahedron
Dodecahedron (convex hull)
Compound of five cubes

Furthermore, it may be viewed as a facetted dodecahedron: the pentagonal faces may be inscribed within the dodecahedron's pentagons. Its dual, the medial triambic icosahedron, is a stellation of the icosahedron.

It is topologically equivalent to a quotient space of the hyperbolic order-6 pentagonal tiling, by distorting the pentagrams back into regular pentagons. As such, it is a regular polyhedron of index two:[2]


See alsoEdit


  1. ^ Maeder, Roman. "41: ditrigonal dodecadodecahedron". MathConsult.
  2. ^ The Regular Polyhedra (of index two), David A. Richter

External linksEdit