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.

Great ditrigonal dodecicosidodecahedron
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
Wythoff symbol	3 5 | 5/3 5/4 3/2 | 5/3
Symmetry group	Ih, [5,3], *532
Index references	U42, C54, W81
Dual polyhedron	Great ditrigonal dodecacronic hexecontahedron
Vertex figure	3.10/3.5.10/3
Bowers acronym	Gidditdid

3D model of a great ditrigonal dodecicosidodecahedron

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).

Truncated dodecahedron

Great icosicosidodecahedron

Great ditrigonal dodecicosidodecahedron

Great dodecicosahedron

See also

• List of uniform polyhedra