This is another 4-dimensional solid projected into 3-space, this one made up of 24 octahedral cells. Also known as the hyperdiamond or octaplex, this in many ways the most interesting of the regular solids in 4-space. Among other properties it is self-dual, and is the regular polytope with no analogue among the five Platonic solids of 3-space.

This model was suggested by Henry Cohn.