, ▁and ▁a ▁suffix ▁(. 2 ) ▁implies ▁mirror ▁symmetry . ▁Similarly ▁Du ▁Val ' s ▁notation ▁has ▁an ▁a ster isk ▁(* ) ▁su pers cript ▁for ▁mirror ▁symmetry . ▁ ▁In volution ▁groups ▁There ▁are ▁five ▁in volution al ▁groups : ▁no ▁symmetry ▁[   ]+ , ▁reflection ▁symmetry ▁[   ], ▁ 2 - fold ▁rot ational ▁symmetry ▁[ 2 ]+ , ▁ 2 - fold ▁rot ore f lection ▁[ 2 + , 2 + ], ▁and ▁central ▁point ▁symmetry ▁[ 2 + , 2 + , 2 + ] ▁as ▁a ▁ 2 - fold ▁double ▁rotation . ▁ ▁Rank ▁ 4 ▁C ox eter ▁groups ▁A ▁pol ych or ic ▁group ▁is ▁one ▁of ▁five ▁symmetry ▁groups ▁of ▁the ▁ 4 - dimensional ▁regular ▁poly top es . ▁There ▁are ▁also ▁three ▁poly hed ral ▁pr ism atic ▁groups , ▁and ▁an ▁infinite ▁set ▁of ▁du op r ism atic ▁groups . ▁Each ▁group ▁defined ▁by ▁a ▁G ours at ▁t etra hed ron ▁fundamental ▁domain ▁bounded ▁by ▁mirror ▁plan es . ▁The ▁di hed ral ▁angles ▁between ▁the ▁mirror s ▁determine ▁order ▁of ▁di hed ral ▁symmetry . ▁The ▁C ox eter – D yn kin ▁diagram ▁is ▁a ▁graph ▁where ▁nodes ▁represent ▁mirror ▁plan es , ▁and ▁edges ▁are ▁called ▁branches , ▁and ▁l abeled ▁by ▁their ▁di hed ral ▁angle ▁order ▁between ▁the ▁mirror s . ▁ ▁The ▁term ▁pol ych or on ▁( pl ural ▁pol ych ora , ▁ad jective ▁pol ych