The angle of the cube, /2, is the basis element that is discarded in the formula for the Dehn invariant, so the Dehn invariant of the cube is zero. More generally, the Dehn invariant of any parallelepiped is also zero. Only one of the two angles of the tetrahedron and octahedron can be included, as the other one is a rational combination of the one that is included and the angle of the cube. The Dehn invariants of each of the other Platonic solids will be a vector in formula_30 formed by multiplying the unit vector for that solid's angle by the length and number of edges of the solid. No matter how they are scaled by different edge lengths, the tetrahedron, icosahedron, and dodecahedron all have Dehn invariants that form vectors pointing in different directions, and therefore are unequal and nonzero.