Face diagonal

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

In geometry, a face diagonal of a polyhedron is a diagonal on one of the faces, in contrast to a space diagonal passing through the interior of the polyhedron.

A cuboid has twelve face diagonals (and four space diagonals); the cuboid's face diagonals can have up to three different lengths (the space diagonals all have the same length). A regular dodecahedron has 60 face diagonals (and 100 space diagonals).

The face diagonal of a cube with side length a is $\sqrt 2a$.