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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,12,4}*1728a
if this polytope has a name.
Group : SmallGroup(1728,46139)
Rank : 5
Schlafli Type : {2,2,12,4}
Number of vertices, edges, etc : 2, 2, 54, 108, 18
Order of s₀s₁s₂s₃s₄ : 6
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 : {2,2,12,4}*864
   3-fold quotients : {2,2,4,4}*576
   6-fold quotients : {2,2,4,4}*288
   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)( 9,10)(12,13)(14,23)(15,25)(16,24)(17,26)(18,28)(19,27)(20,29)
(21,31)(22,30)(33,34)(36,37)(39,40)(41,50)(42,52)(43,51)(44,53)(45,55)(46,54)
(47,56)(48,58)(49,57);;
s3 := ( 5, 6)( 8,24)( 9,23)(10,25)(11,15)(12,14)(13,16)(17,31)(18,30)(19,29)
(21,22)(27,28)(32,33)(35,51)(36,50)(37,52)(38,42)(39,41)(40,43)(44,58)(45,57)
(46,56)(48,49)(54,55);;
s4 := ( 5,35)( 6,37)( 7,36)( 8,32)( 9,34)(10,33)(11,38)(12,40)(13,39)(14,44)
(15,46)(16,45)(17,41)(18,43)(19,42)(20,47)(21,49)(22,48)(23,53)(24,55)(25,54)
(26,50)(27,52)(28,51)(29,56)(30,58)(31,57);;
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, 
s4*s2*s3*s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3*s2*s3, 
s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

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