Polytope of Type {2,60}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,60}*240
if this polytope has a name.
Group : SmallGroup(240,177)
Rank : 3
Schlafli Type : {2,60}
Number of vertices, edges, etc : 2, 60, 60
Order of s₀s₁s₂ : 60
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,60,2} of size 480
   {2,60,4} of size 960
   {2,60,4} of size 960
   {2,60,4} of size 960
   {2,60,6} of size 1440
   {2,60,6} of size 1440
   {2,60,6} of size 1440
   {2,60,6} of size 1440
   {2,60,8} of size 1920
   {2,60,8} of size 1920
   {2,60,4} of size 1920
   {2,60,6} of size 1920
   {2,60,6} of size 1920
   {2,60,4} of size 1920
   {2,60,4} of size 1920
Vertex Figure Of :
   {2,2,60} of size 480
   {3,2,60} of size 720
   {4,2,60} of size 960
   {5,2,60} of size 1200
   {6,2,60} of size 1440
   {7,2,60} of size 1680
   {8,2,60} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,30}*120
   3-fold quotients : {2,20}*80
   4-fold quotients : {2,15}*60
   5-fold quotients : {2,12}*48
   6-fold quotients : {2,10}*40
   10-fold quotients : {2,6}*24
   12-fold quotients : {2,5}*20
   15-fold quotients : {2,4}*16
   20-fold quotients : {2,3}*12
   30-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,60}*480a, {2,120}*480
   3-fold covers : {2,180}*720, {6,60}*720b, {6,60}*720c
   4-fold covers : {4,120}*960a, {4,60}*960a, {4,120}*960b, {8,60}*960a, {8,60}*960b, {2,240}*960, {4,60}*960b
   5-fold covers : {2,300}*1200, {10,60}*1200b, {10,60}*1200c
   6-fold covers : {4,180}*1440a, {2,360}*1440, {6,120}*1440b, {6,120}*1440c, {12,60}*1440b, {12,60}*1440c
   7-fold covers : {14,60}*1680, {2,420}*1680
   8-fold covers : {8,60}*1920a, {4,120}*1920a, {8,120}*1920a, {8,120}*1920b, {8,120}*1920c, {8,120}*1920d, {16,60}*1920a, {4,240}*1920a, {16,60}*1920b, {4,240}*1920b, {4,60}*1920a, {4,120}*1920b, {8,60}*1920b, {2,480}*1920, {4,60}*1920d, {8,60}*1920e, {8,60}*1920f, {4,120}*1920c, {4,120}*1920d
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);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

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

Permutation Representation (Magma) :

s0 := Sym(62)!(1,2);
s1 := Sym(62)!( 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(62)!( 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);
poly := sub<Sym(62)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

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

to this polytope