Great disdyakis dodecahedron

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

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.

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 ${\displaystyle \arccos({\frac {-71+12{\sqrt {2}}}{97}})\approx 123.848\,891\,579\,44^{\circ }}$. Part of each triangle lies within the solid, hence is invisible in solid models.

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

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

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

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