The endodocehedron, also called the concave pyrohedral dodecahedron, is the concave solid corresponding to the interior void formed when each face of a regular dodecahedron is folded along a diagonal and resulting faces are unfolded to form a cube. It is equilateral and has 12 faces, 30 edges, and 20 vertices.
The endodocehedron with unit edge lengths corresponds to removing six square-base oblique wedges of edge length 
(where 
is the golden ratio), height
1/2 and ridge length 1/2 from a cube of edge length 
.
The endododecahedron can be constructed from 6 pieces as shown above, where each edge has unit length, assembled so that the central edges of adjacent pieces are oppositely oriented.
The endododecahedron of edge length 
has surface area
 |
and volume
 |
where 
is again the golden ratio.
The skeleton of the endodecahedron is the dodecahedral graph.
