Polytope of Type {6,2,12,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,12,3}*1152
if this polytope has a name.
Group : SmallGroup(1152,157603)
Rank : 5
Schlafli Type : {6,2,12,3}
Number of vertices, edges, etc : 6, 6, 16, 24, 4
Order of s₀s₁s₂s₃s₄ : 24
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 : {3,2,12,3}*576, {6,2,6,3}*576
   3-fold quotients : {2,2,12,3}*384
   4-fold quotients : {3,2,6,3}*288, {6,2,3,3}*288
   6-fold quotients : {2,2,6,3}*192
   8-fold quotients : {3,2,3,3}*144
   12-fold quotients : {2,2,3,3}*96
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 := ( 7,15)( 8,10)( 9,31)(11,16)(12,54)(13,53)(14,19)(17,48)(18,47)(20,32)
(21,52)(22,50)(23,42)(24,39)(25,38)(26,40)(27,36)(28,41)(29,37)(30,35)(33,46)
(34,45)(43,49)(44,51);;
s4 := ( 7,52)( 8,46)( 9,45)(10,42)(11,54)(12,17)(13,18)(14,50)(15,30)(16,48)
(19,27)(20,47)(21,35)(22,36)(23,33)(24,34)(25,37)(26,51)(28,40)(29,49)(31,39)
(32,53)(38,43)(41,44);;
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, 
s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s4*s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*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)!( 7,15)( 8,10)( 9,31)(11,16)(12,54)(13,53)(14,19)(17,48)(18,47)
(20,32)(21,52)(22,50)(23,42)(24,39)(25,38)(26,40)(27,36)(28,41)(29,37)(30,35)
(33,46)(34,45)(43,49)(44,51);
s4 := Sym(54)!( 7,52)( 8,46)( 9,45)(10,42)(11,54)(12,17)(13,18)(14,50)(15,30)
(16,48)(19,27)(20,47)(21,35)(22,36)(23,33)(24,34)(25,37)(26,51)(28,40)(29,49)
(31,39)(32,53)(38,43)(41,44);
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, s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s4*s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3 >;

to this polytope