▁It ▁is ▁also ▁called ▁a ▁hyper - oct ah ed ral ▁group ▁for ▁extending ▁the ▁ 3 D ▁oct ah ed ral ▁group ▁[ 4 , 3 ], ▁and ▁the ▁t esser actic ▁group ▁for ▁the ▁t esser act , ▁. ▁ ▁The ▁ch iral ▁hex ade c ach or ic ▁group ▁is ▁[ 4 , 3 , 3 ]+ , ▁( ), ▁order ▁ 1 9 2 , ▁( D u ▁Val ▁# 2 7 ▁( O / V ; O / V ), ▁Con way ▁ ± 1 / 6 [ O × O ]). ▁This ▁group ▁represents ▁the ▁construction ▁of ▁an ▁om nis n ub ▁t esser act , ▁, ▁although ▁it ▁can ▁not ▁be ▁made ▁uniform . ▁ ▁The ▁ion ic ▁dimin ished ▁hex ade c ach or ic ▁group ▁is ▁[ 4 ,( 3 , 3 )+ ], ▁( ), ▁order ▁ 1 9 2 , ▁( D u ▁Val ▁# 4 1 ▁( T / V ; T / V )* , ▁Con way ▁ ± 1 / 3 [ T × T ]. 2 ). ▁This ▁group ▁leads ▁to ▁the ▁sn ub ▁ 2 4 - cell ▁with ▁construction ▁. ▁ ▁The ▁half ▁hex ade c ach or ic ▁group ▁is ▁[ 1 + , 4 , 3 , 3 ], ▁( ▁= ▁), ▁order ▁ 1 9 2 , ▁and ▁same ▁as ▁the ▁# dem it esser actic ▁symmetry : ▁[ 3 1 , 1 , 1 ]. ▁This ▁group ▁is ▁expressed ▁in ▁the ▁t