A hexahedron is a polyhedron with six faces. The figure above shows a number of named hexahedra, in particular the acute golden rhombohedron, cube, cuboid, hemicube, hemiobelisk, obtuse golden rhombohedron, pentagonal pyramid, pentagonal wedge, tetragonal antiwedge, and triangular dipyramid.
There are seven topologically distinct convex hexahedra, corresponding through graph duality with the seven polyhedral 6-vertex graphs. The illustration above shows these seven hexahedra (top line), their skeletons (middle line), and the polyhedral 6-vertex graphs whose duals correspond to the polyhedra and their skeletons (bottom line).
An additional hexahedron can be obtained by truncation of two of the four apexes of the tetrahedron, producing a solid composed of two triangles, two quadrilaterals, and two pentagons. Like the cube, it has six faces, eight vertices, twelve edges, and a cubic graph as its skeleton.
The unique regular hexahedron is the cube and the unique chiral hexahedron is the tetragonal antiwedge.
Two hexahedra can be built from regular polygons with equal edge lengths: the equilateral triangular dipyramid and pentagonal pyramid. Rhombohedra are a special class of hexahedron in which opposite faces are congruent rhombi.
Through graph duality, the numbers of vertices in the faces of a hexahedron correspond to the degree
sequence (sequence of vertex degrees) of a polyhedral 6-vertex graph. The following
table lists the hexahedra, together with their degree sequences, number of vertices
, and number of edges 
, which are related through the polyhedral
formula. Standard names do not appear to be in common use for a number of these;
for such cases, the names appearing on Michon are used.
| hexahedron | degree sequence |  |  |
| triangular dipyramid | (3, 3, 3, 3, 3, 3) | 5 | 9 |
| pentagonal pyramid | (3, 3, 3, 3, 3, 5) | 6 | 10 |
| tetragonal antiwedge | (3, 3, 3, 3, 4, 4) | 6 | 10 |
| hemiobelisk | (3, 3, 3, 4, 4, 5) | 7 | 11 |
| hemicube | (3, 3, 4, 4, 4, 4) | 7 | 11 |
| pentagonal wedge | (3, 3, 4, 4, 5, 5) | 8 | 12 |
| cube | (4, 4, 4, 4, 4, 4) | 8 | 12 |
