ated ▁ 8 - sim plex ▁ ▁Altern ate ▁names ▁ ▁Great ▁rh omb ated ▁en ne az et ton ▁( ac ron ym : ▁gr ene ) ▁( J on athan ▁Bow ers ) ▁ ▁Co ordinates ▁ ▁The ▁Cart esian ▁coordinates ▁of ▁the ▁vertices ▁of ▁the ▁cant it run c ated ▁ 8 - sim plex ▁can ▁be ▁most ▁simply ▁position ed ▁in ▁ 9 - space ▁as ▁permut ations ▁of ▁( 0 , 0 , 0 , 0 , 0 , 0 , 1 , 2 , 3 ). ▁This ▁construction ▁is ▁based ▁on ▁fac ets ▁of ▁the ▁b ic ant it run c ated ▁ 9 - orth ople x . ▁ ▁Im ages ▁ ▁B ic ant it run c ated ▁ 8 - sim plex ▁ ▁Altern ate ▁names ▁ ▁Great ▁bir h omb ated ▁en ne az et ton ▁( ac ron ym : ▁gab rene ) ▁( J on athan ▁Bow ers ) ▁ ▁Co ordinates ▁ ▁The ▁Cart esian ▁coordinates ▁of ▁the ▁vertices ▁of ▁the ▁b 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 , 0 , 1 , 2 , 3 , 3 ). ▁This ▁construction ▁is ▁based ▁on ▁fac ets ▁of ▁the ▁b ic ant it run c ated ▁ 9 - orth ople x . ▁ ▁Im ages ▁ ▁Tr ic ant it run c