Polytope of Type {6,2,3,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,3,8}*1152
if this polytope has a name.
Group : SmallGroup(1152,157603)
Rank : 5
Schlafli Type : {6,2,3,8}
Number of vertices, edges, etc : 6, 6, 6, 24, 16
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,3,8}*576, {6,2,3,4}*576
   3-fold quotients : {2,2,3,8}*384
   4-fold quotients : {3,2,3,4}*288, {6,2,3,4}*288
   6-fold quotients : {2,2,3,4}*192
   8-fold quotients : {3,2,3,4}*144, {6,2,3,2}*144
   12-fold quotients : {2,2,3,4}*96
   16-fold quotients : {3,2,3,2}*72
   24-fold quotients : {2,2,3,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (3,4)(5,6);;
s1 := (1,5)(2,3)(4,6);;
s2 := ( 8, 9)(10,11)(12,25)(13,28)(15,20)(16,19)(17,37)(18,40)(21,43)(22,44)
(23,29)(24,26)(27,48)(30,47)(31,32)(33,49)(34,51)(35,38)(36,41)(39,53)(42,54)
(45,46);;
s3 := ( 7,10)( 8,19)( 9,15)(12,48)(13,47)(14,31)(16,20)(17,53)(18,54)(21,46)
(22,45)(23,30)(24,27)(25,26)(28,29)(33,50)(34,52)(35,39)(36,42)(37,38)(40,41)
(43,44);;
s4 := ( 7,50)( 8,46)( 9,45)(10,53)(11,39)(12,40)(13,37)(14,52)(15,48)(16,30)
(17,28)(18,25)(19,47)(20,27)(21,41)(22,38)(23,51)(24,49)(26,33)(29,34)(31,54)
(32,42)(35,44)(36,43);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*s3*s4*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(54)!(3,4)(5,6);
s1 := Sym(54)!(1,5)(2,3)(4,6);
s2 := Sym(54)!( 8, 9)(10,11)(12,25)(13,28)(15,20)(16,19)(17,37)(18,40)(21,43)
(22,44)(23,29)(24,26)(27,48)(30,47)(31,32)(33,49)(34,51)(35,38)(36,41)(39,53)
(42,54)(45,46);
s3 := Sym(54)!( 7,10)( 8,19)( 9,15)(12,48)(13,47)(14,31)(16,20)(17,53)(18,54)
(21,46)(22,45)(23,30)(24,27)(25,26)(28,29)(33,50)(34,52)(35,39)(36,42)(37,38)
(40,41)(43,44);
s4 := Sym(54)!( 7,50)( 8,46)( 9,45)(10,53)(11,39)(12,40)(13,37)(14,52)(15,48)
(16,30)(17,28)(18,25)(19,47)(20,27)(21,41)(22,38)(23,51)(24,49)(26,33)(29,34)
(31,54)(32,42)(35,44)(36,43);
poly := sub<Sym(54)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*s3*s4*s2*s3 >;

to this polytope