Polytope of Type {3,2,20,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,20,6}*1440a
if this polytope has a name.
Group : SmallGroup(1440,5284)
Rank : 5
Schlafli Type : {3,2,20,6}
Number of vertices, edges, etc : 3, 3, 20, 60, 6
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 : {3,2,10,6}*720
   3-fold quotients : {3,2,20,2}*480
   5-fold quotients : {3,2,4,6}*288a
   6-fold quotients : {3,2,10,2}*240
   10-fold quotients : {3,2,2,6}*144
   12-fold quotients : {3,2,5,2}*120
   15-fold quotients : {3,2,4,2}*96
   20-fold quotients : {3,2,2,3}*72
   30-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := ( 5, 8)( 6, 7)(10,13)(11,12)(15,18)(16,17)(20,23)(21,22)(25,28)(26,27)
(30,33)(31,32)(34,49)(35,53)(36,52)(37,51)(38,50)(39,54)(40,58)(41,57)(42,56)
(43,55)(44,59)(45,63)(46,62)(47,61)(48,60);;
s3 := ( 4,35)( 5,34)( 6,38)( 7,37)( 8,36)( 9,45)(10,44)(11,48)(12,47)(13,46)
(14,40)(15,39)(16,43)(17,42)(18,41)(19,50)(20,49)(21,53)(22,52)(23,51)(24,60)
(25,59)(26,63)(27,62)(28,61)(29,55)(30,54)(31,58)(32,57)(33,56);;
s4 := ( 4, 9)( 5,10)( 6,11)( 7,12)( 8,13)(19,24)(20,25)(21,26)(22,27)(23,28)
(34,39)(35,40)(36,41)(37,42)(38,43)(49,54)(50,55)(51,56)(52,57)(53,58);;
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*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, 
s0*s1*s0*s1*s0*s1, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(63)!(2,3);
s1 := Sym(63)!(1,2);
s2 := Sym(63)!( 5, 8)( 6, 7)(10,13)(11,12)(15,18)(16,17)(20,23)(21,22)(25,28)
(26,27)(30,33)(31,32)(34,49)(35,53)(36,52)(37,51)(38,50)(39,54)(40,58)(41,57)
(42,56)(43,55)(44,59)(45,63)(46,62)(47,61)(48,60);
s3 := Sym(63)!( 4,35)( 5,34)( 6,38)( 7,37)( 8,36)( 9,45)(10,44)(11,48)(12,47)
(13,46)(14,40)(15,39)(16,43)(17,42)(18,41)(19,50)(20,49)(21,53)(22,52)(23,51)
(24,60)(25,59)(26,63)(27,62)(28,61)(29,55)(30,54)(31,58)(32,57)(33,56);
s4 := Sym(63)!( 4, 9)( 5,10)( 6,11)( 7,12)( 8,13)(19,24)(20,25)(21,26)(22,27)
(23,28)(34,39)(35,40)(36,41)(37,42)(38,43)(49,54)(50,55)(51,56)(52,57)(53,58);
poly := sub<Sym(63)|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, s0*s1*s0*s1*s0*s1, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

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