Polytope of Type {6,20,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,20,2}*480a
if this polytope has a name.
Group : SmallGroup(480,1088)
Rank : 4
Schlafli Type : {6,20,2}
Number of vertices, edges, etc : 6, 60, 20, 2
Order of s₀s₁s₂s₃ : 60
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,20,2,2} of size 960
   {6,20,2,3} of size 1440
   {6,20,2,4} of size 1920
Vertex Figure Of :
   {2,6,20,2} of size 960
   {3,6,20,2} of size 1440
   {4,6,20,2} of size 1920
   {3,6,20,2} of size 1920
   {4,6,20,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,10,2}*240
   3-fold quotients : {2,20,2}*160
   5-fold quotients : {6,4,2}*96a
   6-fold quotients : {2,10,2}*80
   10-fold quotients : {6,2,2}*48
   12-fold quotients : {2,5,2}*40
   15-fold quotients : {2,4,2}*32
   20-fold quotients : {3,2,2}*24
   30-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,20,4}*960, {6,40,2}*960, {12,20,2}*960
   3-fold covers : {18,20,2}*1440a, {6,20,6}*1440, {6,60,2}*1440a, {6,60,2}*1440b
   4-fold covers : {12,20,4}*1920, {6,20,8}*1920a, {6,40,4}*1920a, {12,40,2}*1920a, {24,20,2}*1920a, {6,20,8}*1920b, {6,40,4}*1920b, {12,40,2}*1920b, {24,20,2}*1920b, {6,20,4}*1920a, {12,20,2}*1920a, {6,80,2}*1920, {6,20,2}*1920a
Permutation Representation (GAP) :

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