Echidnahedron

The "echidnahedron" is the term for the spiky fourth icosahedron stellation (in the enumeration of Maeder 1994) apparently first used in the Netlib polyhedron database.

It is implemented in the Wolfram Language as PolyhedronData["Echidnahedron"].

It has 92 vertices, 270 edges, and 180 faces. Its vertices are arranged in three concentric groups of 20 (indicated in red in the above illustration), 12 (green), and 60 (blue).

For an echidnahedron with edge lengths , , , and (where is the golden ratio), the vertices determine a regular dodecahedron, regular icosahedron, and (irregular) truncated icosahedron, with circumradii

			(1)
			(2)
			(3)

respectively.

The surface area and volume are given by

			(4)
			(5)

A solid echidnahedron has moment of inertia tensor

(6)

for uniform density solid of mass .