Great disdyakis dodecahedron explained

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.

Proportions

The triangles have one angle of

\arccos(	3	+
	4

	1
	8

\sqrt{2}) ≈ 22.06219115754^\circ

, one of

\arccos(-	1	-
	6

	1
	12

\sqrt{2}) ≈ 106.53002715022^\circ

and one of

\arccos(-	1	+
	12

	1
	2

\sqrt{2}) ≈ 51.40778169224^\circ

. The dihedral angle equals

\arccos(	-71+12\sqrt{2

})\approx 123.848\,891\,579\,44^. 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.