Polytope of Type {6,2,4,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,4,12}*1152b
if this polytope has a name.
Group : SmallGroup(1152,157549)
Rank : 5
Schlafli Type : {6,2,4,12}
Number of vertices, edges, etc : 6, 6, 4, 24, 12
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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 : {3,2,4,12}*576b, {6,2,4,6}*576c
   3-fold quotients : {2,2,4,12}*384b
   4-fold quotients : {3,2,4,6}*288c, {6,2,4,3}*288
   6-fold quotients : {2,2,4,6}*192c
   8-fold quotients : {3,2,4,3}*144
   12-fold quotients : {2,2,4,3}*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 := ( 7,12)( 8,16)( 9,19)(10,20)(11,21)(13,27)(14,28)(15,29)(17,33)(18,34)
(22,39)(23,40)(24,38)(25,41)(26,42)(30,51)(31,49)(32,47)(35,48)(36,50)(37,46)
(43,53)(44,54)(45,52);;
s3 := ( 8, 9)(10,11)(12,22)(14,18)(15,17)(16,30)(19,35)(20,38)(21,23)(24,40)
(25,26)(27,43)(28,46)(29,36)(31,34)(32,50)(33,47)(37,49)(41,52)(42,44)(45,54)
(48,51);;
s4 := ( 7,15)( 8,11)( 9,26)(10,14)(12,29)(13,18)(16,21)(17,25)(19,42)(20,28)
(22,32)(23,49)(24,35)(27,34)(30,45)(31,40)(33,41)(36,54)(37,43)(38,48)(39,47)
(44,50)(46,53)(51,52);;
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*s2*s3, s2*s3*s4*s3*s2*s3*s4*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
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)!( 7,12)( 8,16)( 9,19)(10,20)(11,21)(13,27)(14,28)(15,29)(17,33)
(18,34)(22,39)(23,40)(24,38)(25,41)(26,42)(30,51)(31,49)(32,47)(35,48)(36,50)
(37,46)(43,53)(44,54)(45,52);
s3 := Sym(54)!( 8, 9)(10,11)(12,22)(14,18)(15,17)(16,30)(19,35)(20,38)(21,23)
(24,40)(25,26)(27,43)(28,46)(29,36)(31,34)(32,50)(33,47)(37,49)(41,52)(42,44)
(45,54)(48,51);
s4 := Sym(54)!( 7,15)( 8,11)( 9,26)(10,14)(12,29)(13,18)(16,21)(17,25)(19,42)
(20,28)(22,32)(23,49)(24,35)(27,34)(30,45)(31,40)(33,41)(36,54)(37,43)(38,48)
(39,47)(44,50)(46,53)(51,52);
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*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

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