▁ ▁As ▁ ▁observed , ▁the ▁De hn ▁invariant ▁is ▁an ▁invariant ▁for ▁the ▁dis section ▁of ▁poly hed ra , ▁in ▁the ▁sense ▁that ▁cutting ▁up ▁a ▁poly hed ron ▁into ▁smaller ▁poly hed ral ▁pieces ▁and ▁then ▁re ass emb ling ▁them ▁into ▁a ▁different ▁poly hed ron ▁does ▁not ▁change ▁the ▁De hn ▁invariant ▁of ▁the ▁result . ▁Another ▁such ▁invariant ▁is ▁the ▁volume ▁of ▁the ▁poly hed ron . ▁Therefore , ▁if ▁it ▁is ▁possible ▁to ▁dis sect ▁one ▁poly hed ron ▁ ▁into ▁a ▁different ▁poly hed ron ▁, ▁then ▁both ▁ ▁and ▁ ▁must ▁have ▁the ▁same ▁De hn ▁invariant ▁as ▁well ▁as ▁the ▁same ▁volume . ▁ ▁extended ▁this ▁result ▁by ▁prov ing ▁that ▁the ▁volume ▁and ▁the ▁De hn ▁invariant ▁are ▁the ▁only ▁invari ants ▁for ▁this ▁problem . ▁If ▁ ▁and ▁ ▁both ▁have ▁the ▁same ▁volume ▁and ▁the ▁same ▁De hn ▁invariant , ▁it ▁is ▁always ▁possible ▁to ▁dis sect ▁one ▁into ▁the ▁other . ▁ ▁De hn ' s ▁result ▁continues ▁to ▁be ▁valid ▁for ▁spher ical ▁geometry ▁and ▁hyper bol ic ▁geometry . ▁In ▁both ▁of ▁those ▁geomet ries , ▁two ▁poly hed ra ▁that ▁can ▁be ▁cut ▁and ▁re ass emble d ▁into ▁each ▁other ▁must ▁have ▁the ▁same ▁De hn ▁invariant . ▁However , ▁as ▁J essen ▁observed , ▁the ▁extension ▁of ▁Syd ler ' s ▁result ▁to ▁spher ical ▁or ▁hyper bol ic ▁geometry ▁remains ▁open : ▁it ▁is ▁not ▁known ▁whether ▁two ▁spher ical ▁or ▁hyper bol