structural:expansion, information:classification
Property of a centrally symmetric polyhedron in 3-space

Every convex centrally symmetric polyhedron P in R admits a pair of opposite (antipodal) points and a path of length L joining them and lying on the boundary ∂ P of P, satisfying

An alternative formulation is as follows. Any centrally symmetric convex body of surface area A can be squeezed through a noose of length π A {\displaystyle {\sqrt {\pi A}}}, with the tightest fit achieved by a sphere. This property is equivalent to a special case of Pu's inequality (see below), one of the earliest systolic inequalities.