2 - fold ▁g yr ation ▁to ▁the ▁fundamental ▁domain , ▁and ▁this ▁gives ▁an ▁effective ▁C ox eter ▁number ▁of ▁ 2 p , ▁for ▁example ▁the ▁[ 4 , 2 , 4 ] ▁and ▁its ▁full ▁symmetry ▁B 4 , ▁[ 4 , 3 , 3 ] ▁group ▁with ▁C ox eter ▁number ▁ 8 . ▁ ▁The ▁symmetry ▁order ▁is ▁equal ▁to ▁the ▁number ▁of ▁cells ▁of ▁the ▁regular ▁pol ych or on ▁times ▁the ▁symmetry ▁of ▁its ▁cells . ▁The ▁om nit run c ated ▁dual ▁pol ych ora ▁have ▁cells ▁that ▁match ▁the ▁fundamental ▁domains ▁of ▁the ▁symmetry ▁group . ▁ ▁Ch iral ▁sub groups ▁▁ ▁Direct ▁sub groups ▁of ▁the ▁reflect ive ▁ 4 - dimensional ▁point ▁groups ▁are : ▁ ▁Pent ach or ic ▁symmetry ▁▁▁ ▁Pent ach or ic ▁group ▁– ▁A 4 , ▁[ 3 , 3 , 3 ], ▁( ), ▁order ▁ 1 2 0 , ▁( D u ▁Val ▁# 5 1 ' ▁( I † / C 1 ; I / C 1 ) † *, ▁Con way ▁+ 1 / 6 0 [ I × I ]. 2 1 ), ▁named ▁for ▁the ▁ 5 - cell ▁( pent ach or on ), ▁given ▁by ▁ring ed ▁C ox eter ▁diagram ▁. ▁It ▁is ▁also ▁sometimes ▁called ▁the ▁hyper - t etra hed ral ▁group ▁for ▁extending ▁the ▁t etra hed ral ▁group ▁[ 3 , 3 ]. ▁There ▁are ▁ 1 0 ▁mirror ▁hyper plan es ▁in ▁this