"cubic" models

Here is a representative of each of the seven types of hexahedra; the first is the cube and we get the six others from the cube with at most three cuttings.

the canonical models

Only three of the seven types of hexahedra can be built from regular polygons (and thus with edges of same length): the cube (regular hexahedron), and the last two (the pentagonal pyramid and the triangular dipyramid).
Here are the canonical forms of these polyhedra; they are the representatives with the richest symmetries. It's easy to discover that only one of theses polyhedra (the first of the second raw) is chiral (without symmetry plane): it's only symmetry is a half-turn.
Two of these hexahedra are auto-dual: the chiral and the pyramid.

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updated 11-10-2005