# 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 ${\displaystyle a{\sqrt {2}}}$.[4]

## References

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