Polytope of Type {6,6,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6,20}*1440d
if this polytope has a name.
Group : SmallGroup(1440,5871)
Rank : 4
Schlafli Type : {6,6,20}
Number of vertices, edges, etc : 6, 18, 60, 20
Order of s₀s₁s₂s₃ : 30
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   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) :
   3-fold quotients : {2,6,20}*480b
   5-fold quotients : {6,6,4}*288f
   10-fold quotients : {6,3,4}*144
   15-fold quotients : {2,6,4}*96b
   30-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (21,41)(22,42)(23,43)(24,44)(25,45)(26,46)(27,47)(28,48)(29,49)(30,50)
(31,51)(32,52)(33,53)(34,54)(35,55)(36,56)(37,57)(38,58)(39,59)(40,60);;
s1 := ( 1,21)( 2,22)( 3,24)( 4,23)( 5,25)( 6,26)( 7,28)( 8,27)( 9,29)(10,30)
(11,32)(12,31)(13,33)(14,34)(15,36)(16,35)(17,37)(18,38)(19,40)(20,39)(43,44)
(47,48)(51,52)(55,56)(59,60);;
s2 := ( 2, 4)( 5,17)( 6,20)( 7,19)( 8,18)( 9,13)(10,16)(11,15)(12,14)(21,41)
(22,44)(23,43)(24,42)(25,57)(26,60)(27,59)(28,58)(29,53)(30,56)(31,55)(32,54)
(33,49)(34,52)(35,51)(36,50)(37,45)(38,48)(39,47)(40,46);;
s3 := ( 1, 6)( 2, 5)( 3, 8)( 4, 7)( 9,18)(10,17)(11,20)(12,19)(13,14)(15,16)
(21,26)(22,25)(23,28)(24,27)(29,38)(30,37)(31,40)(32,39)(33,34)(35,36)(41,46)
(42,45)(43,48)(44,47)(49,58)(50,57)(51,60)(52,59)(53,54)(55,56);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s2*s3*s2*s3*s2*s1*s3*s2*s3*s2*s3*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(60)!(21,41)(22,42)(23,43)(24,44)(25,45)(26,46)(27,47)(28,48)(29,49)
(30,50)(31,51)(32,52)(33,53)(34,54)(35,55)(36,56)(37,57)(38,58)(39,59)(40,60);
s1 := Sym(60)!( 1,21)( 2,22)( 3,24)( 4,23)( 5,25)( 6,26)( 7,28)( 8,27)( 9,29)
(10,30)(11,32)(12,31)(13,33)(14,34)(15,36)(16,35)(17,37)(18,38)(19,40)(20,39)
(43,44)(47,48)(51,52)(55,56)(59,60);
s2 := Sym(60)!( 2, 4)( 5,17)( 6,20)( 7,19)( 8,18)( 9,13)(10,16)(11,15)(12,14)
(21,41)(22,44)(23,43)(24,42)(25,57)(26,60)(27,59)(28,58)(29,53)(30,56)(31,55)
(32,54)(33,49)(34,52)(35,51)(36,50)(37,45)(38,48)(39,47)(40,46);
s3 := Sym(60)!( 1, 6)( 2, 5)( 3, 8)( 4, 7)( 9,18)(10,17)(11,20)(12,19)(13,14)
(15,16)(21,26)(22,25)(23,28)(24,27)(29,38)(30,37)(31,40)(32,39)(33,34)(35,36)
(41,46)(42,45)(43,48)(44,47)(49,58)(50,57)(51,60)(52,59)(53,54)(55,56);
poly := sub<Sym(60)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s2*s3*s2*s3*s2*s1*s3*s2*s3*s2*s3*s2 >;

References : None.
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