Great disdyakis dodecahedron

In geometry, the great disdyakis dodecahedron is a nonconvex isohedral polyhedron. It is the dual of the uniform great truncated cuboctahedron. It has 48 triangular faces.

Great disdyakis dodecahedron
Type	Star polyhedron
Face
Elements	F = 48, E = 72 V = 26 (χ = 2)
Symmetry group	Oh, [4,3], *432
Index references	DU20
dual polyhedron	Great truncated cuboctahedron

3D model of a great disdyakis dodecahedron

Proportions

The triangles have one angle of ${\displaystyle \arccos({\frac {3}{4}}+{\frac {1}{8}}{\sqrt {2}})\approx 22.062\,191\,157\,54^{\circ }}$, one of ${\displaystyle \arccos(-{\frac {1}{6}}-{\frac {1}{12}}{\sqrt {2}})\approx 106.530\,027\,150\,22^{\circ }}$ and one of ${\displaystyle \arccos(-{\frac {1}{12}}+{\frac {1}{2}}{\sqrt {2}})\approx 51.407\,781\,692\,24^{\circ }}$. The dihedral angle equals ${\displaystyle \arccos({\frac {-71+12{\sqrt {2}}}{97}})\approx 123.848\,891\,579\,44^{\circ }}$.

Related polyhedra

The great disdyakis dodecahedron is topologically identical to the convex Catalan solid, disdyakis dodecahedron, which is dual to the truncated cuboctahedron.

References

• Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 0730208

External links

• Weisstein, Eric W. "Great disdyakis dodecahedron". MathWorld.