Space diagonal

AC' (shown in blue) is a space diagonal, while AC (shown in red) is a face diagonal.

In geometry, a space diagonal (also interior diagonal or body diagonal) of a polyhedron is a line connecting two vertices that are not on the same face. Space diagonals contrast with face diagonals, which connect vertices on the same face (but not on the same edge) as each other.[1]

For example, a pyramid has no space diagonals, while a cube (shown at right) or more generally a parallelepiped has four space diagonals.

  1. ^ William F. Kern, James R Bland,Solid Mensuration with proofs, 1938, p.116