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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,12,6}*1728i
if this polytope has a name.
Group : SmallGroup(1728,47912)
Rank : 5
Schlafli Type : {2,2,12,6}
Number of vertices, edges, etc : 2, 2, 36, 108, 18
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 : {2,2,12,6}*864c
   3-fold quotients : {2,2,4,6}*576
   6-fold quotients : {2,2,4,6}*288
   9-fold quotients : {2,2,12,2}*192
   18-fold quotients : {2,2,6,2}*96
   27-fold quotients : {2,2,4,2}*64
   36-fold quotients : {2,2,3,2}*48
   54-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 7)( 8,14)( 9,16)(10,15)(11,23)(12,25)(13,24)(18,19)(20,26)(21,28)
(22,27)(30,31)(33,34)(35,41)(36,43)(37,42)(38,50)(39,52)(40,51)(45,46)(47,53)
(48,55)(49,54)(57,58);;
s3 := ( 5, 6)( 8,12)( 9,11)(10,13)(14,15)(17,21)(18,20)(19,22)(23,24)(26,30)
(27,29)(28,31)(32,33)(35,39)(36,38)(37,40)(41,42)(44,48)(45,47)(46,49)(50,51)
(53,57)(54,56)(55,58);;
s4 := ( 5,44)( 6,45)( 7,46)( 8,41)( 9,42)(10,43)(11,47)(12,48)(13,49)(14,35)
(15,36)(16,37)(17,32)(18,33)(19,34)(20,38)(21,39)(22,40)(23,53)(24,54)(25,55)
(26,50)(27,51)(28,52)(29,56)(30,57)(31,58);;
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*s1*s0*s1, 
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*s3*s4*s3*s4, 
s2*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*s3*s2*s3, 
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(58)!(1,2);
s1 := Sym(58)!(3,4);
s2 := Sym(58)!( 6, 7)( 8,14)( 9,16)(10,15)(11,23)(12,25)(13,24)(18,19)(20,26)
(21,28)(22,27)(30,31)(33,34)(35,41)(36,43)(37,42)(38,50)(39,52)(40,51)(45,46)
(47,53)(48,55)(49,54)(57,58);
s3 := Sym(58)!( 5, 6)( 8,12)( 9,11)(10,13)(14,15)(17,21)(18,20)(19,22)(23,24)
(26,30)(27,29)(28,31)(32,33)(35,39)(36,38)(37,40)(41,42)(44,48)(45,47)(46,49)
(50,51)(53,57)(54,56)(55,58);
s4 := Sym(58)!( 5,44)( 6,45)( 7,46)( 8,41)( 9,42)(10,43)(11,47)(12,48)(13,49)
(14,35)(15,36)(16,37)(17,32)(18,33)(19,34)(20,38)(21,39)(22,40)(23,53)(24,54)
(25,55)(26,50)(27,51)(28,52)(29,56)(30,57)(31,58);
poly := sub<Sym(58)|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*s1*s0*s1, 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*s3*s4*s3*s4, 
s2*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*s3*s2*s3, 
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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