A hexahedron (plural: hexahedra) is any polyhedron with six faces, although usually implies the cube as a regular hexahedron with all its faces square, and three squares around each vertex.
There are seven topologically distinct convex hexahedra,[1] one of which exists in two mirror image forms. (Two polyhedra are "topologically distinct" if they have intrinsically different arrangements of faces and vertices, such that it is impossible to distort one into the other simply by changing the lengths of edges or the angles between edges or faces.)
| Quadrilaterally-faced hexahedra 46 faces, 12 edges, 8 vertices |
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Parallelepiped (three pairs of parallelograms) |
Rhombohedron (three pairs of rhombi) |
Trigonal trapezohedron (congruent rhombi) |
Cuboid (three pairs of rectangles) |
Cube (square) |
Quadrilateral frustum (apex-truncated square pyramid) |
| Others | |||||
Pentagonal pyramid (5.35) Faces 10 E, 6 V |
Triangular dipyramid 36 Faces 9 E, 5 V |
5.4.4.3.3.3 Faces 11 E, 7 V |
5.5.4.4.3.3 Faces 12 E, 8 V |
4.4.4.4.3.3 Faces 11 E, 7 V |
Tetragonal antiwedge. Chiral – exists in "left-handed" and "right-handed" mirror image forms. 4.4.3.3.3.3 Faces 10 E, 6 V |
There are three further topologically distinct hexahedra that can only be realised as concave figures:
4.4.3.3.3.3 Faces 10 E, 6 V |
6.6.3.3.3.3 Faces 12 E, 8 V |
5.5.3.3.3.3 Faces 11 E, 7 V |
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