# Great ditrigonal dodecicosidodecahedron

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}
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

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.

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

## References

1. ^ Maeder, Roman. "42: great ditrigonal dodecicosidodecahedron". MathConsult.