For a regular -gon
with inradius , the area is given by

(4)

edge length by

(5)

and the perimeter is given by

(6)

Thus,

(7)

which converges to 1 for .

The isoperimetric quotient can similarly be defined for a polyhedron, where it is defined as the dimensionless quantity obtained using the volume ()
and surface area () of the sphere as a reference,