▁around ▁each ▁vertex ▁in ▁an ▁order - 6 ▁square ▁t iling ▁vertex ▁arrangement . ▁ ▁It ▁has ▁a ▁second ▁construction ▁as ▁a ▁uniform ▁h oney comb , ▁Sch lä fli ▁symbol ▁{ 4 ,( 4 , 3 , 4 )}, ▁C ox eter ▁diagram , ▁, ▁with ▁altern ating ▁types ▁or ▁colors ▁of ▁square ▁t iling ▁cells . ▁In ▁C ox eter ▁notation ▁the ▁half ▁symmetry ▁is ▁[ 4 , 4 , 6 , 1 + ] ▁= ▁[ 4 , (( 4 , 3 , 4 )) ]. ▁ ▁Order - 4 - in finite ▁square ▁h oney comb ▁ ▁In ▁the ▁geometry ▁of ▁hyper bol ic ▁ 3 - space , ▁the ▁order - 4 - in finite ▁square ▁h oney comb ▁is ▁a ▁regular ▁space - fill ing ▁t ess ell ation ▁( or ▁h oney comb ) ▁with ▁Sch lä fli ▁symbol ▁{ 4 , 4 , ∞ }. ▁It ▁has ▁infinitely ▁many ▁square ▁t iling , ▁{ 4 , 4 }, ▁around ▁each ▁edge . ▁All ▁vertices ▁are ▁ult ra - ide al ▁( ex isting ▁beyond ▁the ▁ideal ▁boundary ) ▁with ▁infinitely ▁many ▁square ▁t iling ▁existing ▁around ▁each ▁vertex ▁in ▁an ▁infinite - order ▁square ▁t iling ▁vertex ▁arrangement . ▁ ▁It ▁has ▁a ▁second ▁construction ▁as ▁a ▁uniform ▁h oney comb , ▁Sch lä fli ▁symbol ▁{ 4 ,( 4 , ∞ , 4 )}, ▁C ox eter ▁diagram , ▁ ▁= ▁, ▁with ▁altern ating ▁types ▁or ▁colors ▁of ▁square ▁t iling ▁cells .