▁group ▁and ▁is ▁ 3 D ▁oct ah ed ral ▁symmetry , ▁[ 4 , 3 ]. ▁A ▁cub ic ▁py ram id ▁can ▁have ▁this ▁symmetry , ▁with ▁Sch lä fli ▁symbol : ▁(   ) ▁ ∨ ▁{ 4 , 3 }. ▁ ▁A ▁ch iral ▁half ▁subgroup ▁[( 4 , 3 )+ , 2 , 1 + ] ▁= ▁[ 4 , 3 , 1 ]+ ▁= ▁[ 4 , 3 ]+ , ▁( ▁= ▁), ▁order ▁ 2 4 ▁( D u ▁Val ▁# 2 6 b ' ▁( O / C 1 ; O / C 1 ), ▁Con way ▁+ 1 / 2 4 [ O × O ]). ▁This ▁is ▁the ▁ 3 D ▁ch iral ▁oct ah ed ral ▁group , ▁[ 4 , 3 ]+ . ▁A ▁sn ub ▁cub ic ▁py ram id ▁can ▁have ▁this ▁symmetry , ▁with ▁Sch lä fli ▁symbol : ▁(   ) ▁ ∨ ▁sr { 4 , 3 }. ▁ ▁Another ▁high - index ▁reflect ive ▁subgroup ▁is ▁the ▁pr ism atic ▁t etra hed ral ▁symmetry , ▁[ 3 , 3 , 2 ], ▁( ), ▁order ▁ 4 8 , ▁subgroup ▁index ▁ 8 , ▁( D u ▁Val ▁# 4 0 b " ▁( O / C 1 ; O / C 1 )* , ▁Con way ▁+ 1 / 2 4 [ O × ]. 2 3 ). ▁ ▁The ▁ch iral ▁subgroup ▁is ▁[ 3 , 3 , 2 ]+ , ▁(