Polytope of Type {2,60,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,60,2}*480
if this polytope has a name.
Group : SmallGroup(480,1167)
Rank : 4
Schlafli Type : {2,60,2}
Number of vertices, edges, etc : 2, 60, 60, 2
Order of s₀s₁s₂s₃ : 60
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,60,2,2} of size 960
   {2,60,2,3} of size 1440
   {2,60,2,4} of size 1920
Vertex Figure Of :
   {2,2,60,2} of size 960
   {3,2,60,2} of size 1440
   {4,2,60,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,30,2}*240
   3-fold quotients : {2,20,2}*160
   4-fold quotients : {2,15,2}*120
   5-fold quotients : {2,12,2}*96
   6-fold quotients : {2,10,2}*80
   10-fold quotients : {2,6,2}*48
   12-fold quotients : {2,5,2}*40
   15-fold quotients : {2,4,2}*32
   20-fold quotients : {2,3,2}*24
   30-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,60,4}*960a, {4,60,2}*960a, {2,120,2}*960
   3-fold covers : {2,180,2}*1440, {2,60,6}*1440b, {2,60,6}*1440c, {6,60,2}*1440b, {6,60,2}*1440c
   4-fold covers : {4,60,4}*1920a, {2,60,8}*1920a, {8,60,2}*1920a, {2,120,4}*1920a, {4,120,2}*1920a, {2,60,8}*1920b, {8,60,2}*1920b, {2,120,4}*1920b, {4,120,2}*1920b, {2,60,4}*1920a, {4,60,2}*1920a, {2,240,2}*1920, {2,60,4}*1920b, {4,60,2}*1920b
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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