Space diagonal

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.

For example, in a cube with edge length a, all four space diagonals are axial diagonals, of common length

More generally, a cuboid with edge lengths a, b, and c has all four space diagonals axial, with common length

A regular octahedron has 3 axial diagonals, of length

A regular icosahedron has 6 axial diagonals of length

[2] A magic square is an arrangement of numbers in a square grid so that the sum of the numbers along every row, column, and diagonal is the same.

Similarly, one may define a magic cube to be an arrangement of numbers in a cubical grid so that the sum of the numbers on the four space diagonals must be the same as the sum of the numbers in each row, each column, and each pillar.