Great ditrigonal dodecicosidodecahedron

Great ditrigonal dodecicosidodecahedron
File:Great ditrigonal dodecicosidodecahedron.png
Type	Uniform star polyhedron
Elements	F = 44, E = 120 V = 60 (χ = −16)
Faces by sides	20{3}+12{5}+12{10/3}
Coxeter diagram	Template:CDD
Wythoff symbol	5/3 5/4 3/2 \| 5/3
Symmetry group	I_h, [5,3], *532
Index references	U₄₂, C₅₄, W₈₁
Dual polyhedron	Great ditrigonal dodecacronic hexecontahedron
Vertex figure	File:Great ditrigonal dodecicosidodecahedron vertfig.png 3.10/3.5.10/3
Bowers acronym	Gidditdid

3D model of a 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.^[1] Its vertex figure is an isosceles trapezoid.

Related polyhedra

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).

File:Truncated dodecahedron.png Truncated dodecahedron	File:Great icosicosidodecahedron.png Great icosicosidodecahedron	File:Great ditrigonal dodecicosidodecahedron.png Great ditrigonal dodecicosidodecahedron	File:Great dodecicosahedron.png Great dodecicosahedron