Polytope of Type {6,2,60}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,60}*1440
if this polytope has a name.
Group : SmallGroup(1440,5676)
Rank : 4
Schlafli Type : {6,2,60}
Number of vertices, edges, etc : 6, 6, 60, 60
Order of s₀s₁s₂s₃ : 60
Order of s₀s₁s₂s₃s₂s₁ : 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 : {3,2,60}*720, {6,2,30}*720
   3-fold quotients : {6,2,20}*480, {2,2,60}*480
   4-fold quotients : {3,2,30}*360, {6,2,15}*360
   5-fold quotients : {6,2,12}*288
   6-fold quotients : {3,2,20}*240, {6,2,10}*240, {2,2,30}*240
   8-fold quotients : {3,2,15}*180
   9-fold quotients : {2,2,20}*160
   10-fold quotients : {3,2,12}*144, {6,2,6}*144
   12-fold quotients : {3,2,10}*120, {6,2,5}*120, {2,2,15}*120
   15-fold quotients : {2,2,12}*96, {6,2,4}*96
   18-fold quotients : {2,2,10}*80
   20-fold quotients : {3,2,6}*72, {6,2,3}*72
   24-fold quotients : {3,2,5}*60
   30-fold quotients : {3,2,4}*48, {2,2,6}*48, {6,2,2}*48
   36-fold quotients : {2,2,5}*40
   40-fold quotients : {3,2,3}*36
   45-fold quotients : {2,2,4}*32
   60-fold quotients : {2,2,3}*24, {3,2,2}*24
   90-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (3,4)(5,6);;
s1 := (1,5)(2,3)(4,6);;
s2 := ( 8, 9)(10,11)(12,13)(15,20)(16,19)(17,22)(18,21)(23,26)(24,25)(27,28)
(29,30)(31,32)(33,42)(34,41)(35,40)(36,39)(37,44)(38,43)(45,48)(46,47)(49,52)
(50,51)(53,54)(55,62)(56,61)(57,60)(58,59)(63,66)(64,65);;
s3 := ( 7,33)( 8,23)( 9,49)(10,17)(11,35)(12,15)(13,55)(14,39)(16,25)(18,45)
(19,31)(20,51)(21,29)(22,63)(24,37)(26,57)(27,34)(28,56)(30,41)(32,59)(36,47)
(38,46)(40,53)(42,65)(43,50)(44,64)(48,58)(52,61)(54,60)(62,66);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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*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*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(66)!(3,4)(5,6);
s1 := Sym(66)!(1,5)(2,3)(4,6);
s2 := Sym(66)!( 8, 9)(10,11)(12,13)(15,20)(16,19)(17,22)(18,21)(23,26)(24,25)
(27,28)(29,30)(31,32)(33,42)(34,41)(35,40)(36,39)(37,44)(38,43)(45,48)(46,47)
(49,52)(50,51)(53,54)(55,62)(56,61)(57,60)(58,59)(63,66)(64,65);
s3 := Sym(66)!( 7,33)( 8,23)( 9,49)(10,17)(11,35)(12,15)(13,55)(14,39)(16,25)
(18,45)(19,31)(20,51)(21,29)(22,63)(24,37)(26,57)(27,34)(28,56)(30,41)(32,59)
(36,47)(38,46)(40,53)(42,65)(43,50)(44,64)(48,58)(52,61)(54,60)(62,66);
poly := sub<Sym(66)|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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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*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*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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