▁in ▁the ▁product ▁represent ▁height ▁and ▁width ▁of ▁rect angles . ▁The ▁invariant ▁for ▁any ▁given ▁polygon ▁is ▁calculated ▁by ▁cutting ▁the ▁polygon ▁into ▁rect angles , ▁taking ▁the ▁tensor ▁product ▁of ▁the ▁height ▁and ▁width ▁of ▁each ▁rectangle , ▁and ▁adding ▁the ▁results . ▁Again , ▁a ▁dis section ▁is ▁possible ▁if ▁and ▁only ▁if ▁two ▁pol yg ons ▁have ▁the ▁same ▁area ▁and ▁the ▁same ▁invariant . ▁ ▁F lex ible ▁poly hed ra ▁are ▁a ▁class ▁of ▁poly hed ra ▁that ▁can ▁under go ▁a ▁continuous ▁motion ▁that ▁pres erves ▁the ▁shape ▁of ▁their ▁faces . ▁By ▁C auch y ' s ▁rig id ity ▁theorem , ▁they ▁must ▁be ▁non - con vex , ▁and ▁it ▁is ▁known ▁( the ▁" bell ows ▁theorem ") ▁that ▁the ▁volume ▁of ▁the ▁poly hed ron ▁must ▁stay ▁constant ▁throughout ▁this ▁motion . ▁A ▁stronger ▁version ▁of ▁this ▁theorem ▁states ▁that ▁the ▁De hn ▁invariant ▁of ▁such ▁a ▁poly hed ron ▁must ▁also ▁remain ▁invariant ▁throughout ▁any ▁continuous ▁motion . ▁This ▁result ▁is ▁called ▁the ▁" strong ▁bell ows ▁theorem ". ▁It ▁has ▁been ▁proven ▁for ▁all ▁non - self - inter sect ing ▁flexible ▁poly hed ra . ▁However , ▁for ▁more ▁complicated ▁flexible ▁poly hed ra ▁with ▁self - inter sections ▁the ▁De hn ▁invariant ▁may ▁change ▁continu ously ▁as ▁the ▁poly hed ron ▁flex es . ▁ ▁The ▁total ▁mean ▁curv ature ▁of ▁a ▁poly hed ral ▁surface ▁has ▁been ▁defined ▁as ▁the ▁sum ▁over ▁the ▁edges ▁of ▁the