Polytope of Type {2,2,60}

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

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

Permutation Representation (Magma) :

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

to this polytope