ub ▁ 2 4 - cell , ▁, ▁although ▁it ▁can ▁not ▁be ▁made ▁uniform . ▁The ▁ion ic ▁dimin ished ▁ icos itet ra chor ic ▁groups , ▁[ 3 + , 4 , 3 ] ▁and ▁[ 3 , 4 , 3 + ], ▁( ▁or ▁), ▁have ▁order ▁ 5 7 6 , ▁( D u ▁Val ▁# 4 3 ▁( T / T ; T / T )* , ▁Con way ▁ ± [ T × T ]. 2 ). ▁This ▁group ▁leads ▁to ▁the ▁sn ub ▁ 2 4 - cell ▁with ▁construction ▁ ▁or ▁. ▁The ▁double ▁dimin ished ▁ icos itet ra chor ic ▁group , ▁[ 3 + , 4 , 3 + ] ▁( the ▁double ▁dimin ishing ▁can ▁be ▁shown ▁by ▁a ▁gap ▁in ▁the ▁diagram ▁ 4 - branch : ▁), ▁order ▁ 2 8 8 , ▁( D u ▁Val ▁# 2 0 ▁( T / T ; T / T ), ▁Con way ▁ ± [ T × T ]) ▁is ▁the ▁commut ator ▁subgroup ▁of ▁[ 3 , 4 , 3 ]. ▁▁ ▁It ▁can ▁be ▁extended ▁as ▁[[ 3 + , 4 , 3 + ]], ▁() ▁order ▁ 5 7 6 , ▁( D u ▁Val ▁# 2 3 ▁( T / T ; O / O ), ▁Con way ▁ ± [ O x T ]). ▁ ▁The ▁ch iral ▁ icos itet ra chor ic ▁group ▁is ▁[ 3 , 4 , 3 ]+ ,