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Polytope of Type {5,2,6,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,6,12}*1440a
if this polytope has a name.
Group : SmallGroup(1440,5282)
Rank : 5
Schlafli Type : {5,2,6,12}
Number of vertices, edges, etc : 5, 5, 6, 36, 12
Order of s0s1s2s3s4 : 60
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 : {5,2,6,6}*720a
   3-fold quotients : {5,2,2,12}*480, {5,2,6,4}*480a
   6-fold quotients : {5,2,2,6}*240, {5,2,6,2}*240
   9-fold quotients : {5,2,2,4}*160
   12-fold quotients : {5,2,2,3}*120, {5,2,3,2}*120
   18-fold quotients : {5,2,2,2}*80
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := ( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)(34,35)
(37,38)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56)(58,59)(61,62)(64,65)(67,68)
(70,71)(73,74)(76,77);;
s3 := ( 6,43)( 7,42)( 8,44)( 9,49)(10,48)(11,50)(12,46)(13,45)(14,47)(15,52)
(16,51)(17,53)(18,58)(19,57)(20,59)(21,55)(22,54)(23,56)(24,70)(25,69)(26,71)
(27,76)(28,75)(29,77)(30,73)(31,72)(32,74)(33,61)(34,60)(35,62)(36,67)(37,66)
(38,68)(39,64)(40,63)(41,65);;
s4 := ( 6,63)( 7,64)( 8,65)( 9,60)(10,61)(11,62)(12,66)(13,67)(14,68)(15,72)
(16,73)(17,74)(18,69)(19,70)(20,71)(21,75)(22,76)(23,77)(24,45)(25,46)(26,47)
(27,42)(28,43)(29,44)(30,48)(31,49)(32,50)(33,54)(34,55)(35,56)(36,51)(37,52)
(38,53)(39,57)(40,58)(41,59);;
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*s4*s3*s2*s3*s4*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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(77)!(2,3)(4,5);
s1 := Sym(77)!(1,2)(3,4);
s2 := Sym(77)!( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)
(34,35)(37,38)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56)(58,59)(61,62)(64,65)
(67,68)(70,71)(73,74)(76,77);
s3 := Sym(77)!( 6,43)( 7,42)( 8,44)( 9,49)(10,48)(11,50)(12,46)(13,45)(14,47)
(15,52)(16,51)(17,53)(18,58)(19,57)(20,59)(21,55)(22,54)(23,56)(24,70)(25,69)
(26,71)(27,76)(28,75)(29,77)(30,73)(31,72)(32,74)(33,61)(34,60)(35,62)(36,67)
(37,66)(38,68)(39,64)(40,63)(41,65);
s4 := Sym(77)!( 6,63)( 7,64)( 8,65)( 9,60)(10,61)(11,62)(12,66)(13,67)(14,68)
(15,72)(16,73)(17,74)(18,69)(19,70)(20,71)(21,75)(22,76)(23,77)(24,45)(25,46)
(26,47)(27,42)(28,43)(29,44)(30,48)(31,49)(32,50)(33,54)(34,55)(35,56)(36,51)
(37,52)(38,53)(39,57)(40,58)(41,59);
poly := sub<Sym(77)|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*s4*s3*s2*s3*s4*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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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