# 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 exterior angles divided by . The density of a regular polygon {*p*/*q*} is *q*. Examples: {5}(regular pentagon) has the density of ; {7/3}(regular great heptagram) has the density of .

For polyhedra, density is equal to its total curvature (the sum of its angular defects) divided by . Examples: {5,3}(regular dodecahedron) has the density of ; {5/2,5}(small stellated dodecahedron) has the density of ; {5/2,3}(great stellated dodecahedron) has the density of . If its faces and vertex figures are non-self-intersecting, the density is also half the Euler characteristic.