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

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

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