Cuboid

In geometry, a cuboid is a hexahedron, a six-faced solid. Its faces are quadrilaterals. Cuboid means "like a cube", in the sense that by adjusting the lengths of the edges or the angles between faces, a cuboid can be transformed into a cube. In mathematical language a cuboid is a convex polyhedron whose polyhedral graph is the same as that of a cube.

A special case of a cuboid is a rectangular cuboid, with six rectangles as faces and adjacent faces meeting at right angles. A cube is a special case of a rectangular cuboid, with six square faces meeting at right angles.

By Euler's formula the numbers of faces F, of vertices V, and of edges E of any convex polyhedron are related by the formula

In the case of a cuboid this gives 6 + 8 – 12 = 2; that is, like a cube, a cuboid has six faces, eight vertices, and twelve edges. Along with the rectangular cuboids, any parallelepiped is a cuboid of this type, as is a square frustum (the shape formed by truncation of the apex of a square pyramid).