Ditrigonal icosahedron

The ditrigonal icosahedron, or ditti, also called the excavated dodecahedron, is a noble self-dual semi-uniform polyhedron. It consists of 20 propeller tripods, with six joining at a vertex. It has two lengths of edges, but it has no degrees of variance; the longer edges are $$\frac{3+\sqrt5}{2} ≈ 2.61803$$ times the length of the shorter edges. The longer edges are also the edges of a great stellated dodecahedron, while the shorter edges are the edges of a dodecahedron. It is a stellation of the icosahedron.

This polyhedron is abstractly regular, being a quotient of the order-6 hexagonal tiling. Its realization may also be considered regular if one also counts conjugacies as symmetries.

Extending the shorter edges while keeping the face planes results in a great icosahedron, while contracting the longer edges while keeping the face planes results in an icosahedron. Relatedly, it can be constructed by antitruncating the icosahedron or hypertruncating the great icosahedron until the resulting pentagons or pentagrams meet, causing the polyhedron to be exotic. Removing the pentagons or pentagrams (which form the faces of a dodecahedron or great stellated dodecahedron) results in the ditrigonal icosahedron.

This polyhedron appears as the vertex figure of the uniform invertidodecahedronary hecatonicosachoron.