# 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.[1]

A cuboid has twelve face diagonals (and four space diagonals);[2] 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).[3]

The face diagonal of a cube with side length a is $a\sqrt 2$.[4]

## References

1. ^ Gullberg, Jan (1997), Mathematics: From the Birth of Numbers, W. W. Norton & Company, p. 396, ISBN 9780393040029.
2. ^ Mullan, Edward C. K. (2003), New Maths in Action, Nelson Thornes, p. 220, ISBN 9780748765195.
3. ^ Sutton, Daud (2002), Platonic & Archimedean Solids, Wooden Books, Bloomsbury Publishing USA, p. 55, ISBN 9780802713865.
4. ^ Messler, Robert W., Jr. (2010), The Essence of Materials for Engineers, Jones & Bartlett Publishers, p. 56, ISBN 9780763778330.