Escher's Solid

"Escher's solid" is the solid illustrated on the right pedestal in M. C. Escher's Waterfall woodcut (Bool et al. 1982, p. 323). It is obtained by augmenting a rhombic dodecahedron until incident edges become parallel, corresponding to augmentation height of for a rhombic dodecahedron with unit edge lengths.

It is the hull of the first rhombic dodecahedron stellation and is a space-filling polyhedron. Its convex hull is a cuboctahedron.

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

It has edge lengths

			(1)
			(2)

surface area and volume

			(3)
			(4)

and moment of inertia tensor

(5)

The skeleton of Escher's solid is the graph of the disdyakis dodecahedron.

Escher's solid also corresponds to the hull of a polyhedron compound of three square dipyramids (nonregular octahedra) with edges of length 2 and .