ated ▁ 8 - sim plex ▁▁ ▁Great ▁tri rh omb ated ▁en ne az et ton ▁( ac ron ym : ▁gat rene ) ▁( J on athan ▁Bow ers ) ▁ ▁Co ordinates ▁ ▁The ▁Cart esian ▁coordinates ▁of ▁the ▁vertices ▁of ▁the ▁tr ic ant it run c ated ▁ 8 - sim plex ▁can ▁be ▁most ▁simply ▁position ed ▁in ▁ 9 - space ▁as ▁permut ations ▁of ▁( 0 , 0 , 0 , 0 , 1 , 2 , 3 , 3 , 3 ). ▁This ▁construction ▁is ▁based ▁on ▁fac ets ▁of ▁the ▁b ic ant it run c ated ▁ 9 - orth ople x . ▁ ▁Im ages ▁ ▁Rel ated ▁poly top es ▁▁ ▁This ▁poly to pe ▁is ▁one ▁of ▁ 1 3 5 ▁uniform ▁ 8 - poly top es ▁with ▁A 8 ▁symmetry . ▁ ▁Notes ▁ ▁References ▁ ▁H . S . M . ▁C ox eter : ▁▁ ▁H . S . M . ▁C ox eter , ▁Reg ular ▁Poly top es , ▁ 3 rd ▁Edition , ▁D over ▁New ▁York , ▁ 1 9 7 3 ▁▁ ▁K ale idos cop es : ▁Selected ▁Writ ings ▁of ▁H . S . M . ▁C ox eter , ▁edited ▁by ▁F . ▁Arthur ▁Sh erk , ▁Peter ▁Mc M ull en , ▁Anthony ▁C . ▁Thompson , ▁Asia ▁I vic ▁We iss , ▁W iley - In ters cience ▁Public ation , ▁ 1 9 9