Property of A Centrally Symmetric Polyhedron in 3-space
Every convex centrally symmetric polyhedron P in R3 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, 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.
Read more about this topic: Systolic Geometry
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