Density

The density of an orientable polytope is an integer that generalizes the concept of a turning number of a polygon. Density is well-defined for orientable uniform polytopes with no faces passing through the center (as in the hemipolyhedra), but standardization of density is poor for general polytopes, especially those without a well-defined center.

For polygons, density is equal to the sum of interior angles divided by $$2\pi$$. The density of a regular polygon {p/q} is q.

For polyhedra, density is equal to its total curvature (the sum of its angular defects) divided by $$4\pi$$. If its faces and vertex figures are non-self-intersecting, the density is also half the Euler characteristic.