"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
![I=[5/9 0 0; 0 5/9 0; 0 0 5/9]Ma^2.](/images/equations/EschersSolid/NumberedEquation1.svg) |
(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 
.
