# Density

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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.

## Polygon density[edit | edit source]

For polygons, density is equal to the sum of exterior angles divided by . The density of a regular polygon , where is an irreducible fraction, is q .

### Examples[edit | edit source]

## Polyhedron density[edit | edit source]

For polyhedra, density is equal to its total curvature (the sum of its angular defects) divided by .

If the faces and vertex figures of a polyhedron are non-self-intersecting, the density is also half the Euler characteristic.