: ▁(   ) ▁ ∨ ▁{ 3 , 3 }. ▁ ▁The ▁ch iral ▁half ▁subgroup ▁[( 3 , 3 )+ , 2 , 1 + ] ▁= ▁[ 3 , 3 ]+ ( ▁= ▁), ▁order ▁ 1 2 , ▁( D u ▁Val ▁# 2 1 b ' ▁( T / C 1 ; T / C 1 ), ▁Con way ▁+ 1 / 1 2 [ T × T ]). ▁This ▁is ▁the ▁ 3 D ▁ch iral ▁t etra hed ral ▁group , ▁[ 3 , 3 ]+ . ▁ ▁A ▁sn ub ▁t etra hed ral ▁py ram id ▁can ▁have ▁this ▁symmetry , ▁with ▁Sch lä fli ▁symbol : ▁(   ) ▁ ∨ ▁sr { 3 , 3 }. ▁ ▁Another ▁high - index ▁radial ▁reflect ive ▁subgroup ▁is ▁[ 4 ,( 3 , 3 )* ], ▁index ▁ 2 4 , ▁removes ▁mirror s ▁with ▁order - 3 ▁di hed ral ▁angles , ▁creating ▁[ 2 , 2 , 2 ] ▁( ), ▁order ▁ 1 6 . ▁O thers ▁are ▁[ 4 , 2 , 4 ] ▁( ), ▁[ 4 , 2 , 2 ] ▁( ), ▁with ▁subgroup ▁indices ▁ 6 ▁and ▁ 1 2 , ▁order ▁ 6 4 ▁and ▁ 3 2 . ▁These ▁groups ▁are ▁lower ▁symmet ries ▁of ▁the ▁t esser act : ▁( ), ▁( ), ▁and ▁( ). ▁These ▁groups ▁are ▁# du op r ism atic ▁symmetry . ▁ ▁I cos itet ra chor