hexahedra

Hexahedron is a polyhedron with six faces. The name comes from Greek, with hex- meaning six and hedra meaning faces or sides. The term is descriptive rather than referring to a single shape, so a hexahedron can be convex or non-convex and may have faces of various polygonal shapes.

The most familiar example is the cube, a regular hexahedron with six square faces, eight vertices, and twelve edges. The cube is a special case among hexahedra and is one of the five Platonic solids. Other six-faced polyhedra include the pentagonal pyramid, which has one pentagonal base and five triangular side faces, giving six faces in total. In general, a convex hexahedron need not resemble a cube and can have different combinations of face types.

Using Euler’s formula for polyhedra, a convex hexahedron satisfies V − E + 6 = 2, which implies E = V + 4. For example, the cube has V = 8 and E = 12. This relationship constrains possible structures, though many distinct combinatorial forms exist for six-faced solids.

Hexahedron is a standard term in geometry and crystallography for any six-faced solid. The cube represents the regular case, but the broader concept encompasses a variety of irregular shapes as well, making it a common primitive in computer graphics and geometric modeling.