ic ▁symmetry ▁ ▁I cos itet ra chor ic ▁group ▁– ▁F 4 , ▁[ 3 , 4 , 3 ], ▁( ), ▁order ▁ 1 1 5 2 , ▁( D u ▁Val ▁# 4 5 ▁( O / T ; O / T )* , ▁Con way ▁[ O × O ]. 2 3 ), ▁named ▁for ▁the ▁ 2 4 - cell ▁( icos itet ra chor on ), ▁. ▁There ▁are ▁ 2 4 ▁mirror ▁plan es ▁in ▁this ▁symmetry , ▁which ▁can ▁be ▁decom posed ▁into ▁two ▁orthogonal ▁sets ▁of ▁ 1 2 ▁mirror s ▁in ▁dem it esser actic ▁symmetry ▁[ 3 1 , 1 , 1 ] ▁sub groups , ▁as ▁[ 3 *, 4 , 3 ] ▁and ▁[ 3 , 4 , 3 * ], ▁as ▁index ▁ 6 ▁sub groups . ▁The ▁extended ▁ icos itet ra chor ic ▁group , ▁Aut ( F 4 ), ▁, ▁() ▁has ▁order ▁ 2 3 0 4 , ▁( D u ▁Val ▁# 4 8 ▁( O / O ; O / O )* , ▁Con way ▁ ± [ O × O ]. 2 ). ▁ ▁The ▁ch iral ▁extended ▁ icos itet ra chor ic ▁group , ▁+ , ▁() ▁has ▁order ▁ 1 1 5 2 , ▁( D u ▁Val ▁# 2 5 ▁( O / O ; O / O ), ▁Con way ▁ ± [ O x O ]). ▁This ▁group ▁represents ▁the ▁construction ▁of ▁the ▁om nis n