Polytope of Type {6,20,2,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,20,2,4}*1920a
if this polytope has a name.
Group : SmallGroup(1920,208127)
Rank : 5
Schlafli Type : {6,20,2,4}
Number of vertices, edges, etc : 6, 60, 20, 4, 4
Order of s₀s₁s₂s₃s₄ : 60
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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 : {6,20,2,2}*960a, {6,10,2,4}*960
   3-fold quotients : {2,20,2,4}*640
   4-fold quotients : {6,10,2,2}*480
   5-fold quotients : {6,4,2,4}*384a
   6-fold quotients : {2,20,2,2}*320, {2,10,2,4}*320
   10-fold quotients : {6,2,2,4}*192, {6,4,2,2}*192a
   12-fold quotients : {2,5,2,4}*160, {2,10,2,2}*160
   15-fold quotients : {2,4,2,4}*128
   20-fold quotients : {3,2,2,4}*96, {6,2,2,2}*96
   24-fold quotients : {2,5,2,2}*80
   30-fold quotients : {2,2,2,4}*64, {2,4,2,2}*64
   40-fold quotients : {3,2,2,2}*48
   60-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
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 := (62,63);;
s4 := (61,62)(63,64);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s2*s1*s0*s1*s2*s1, s3*s4*s3*s4*s3*s4*s3*s4, 
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(64)!( 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(64)!( 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(64)!( 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(64)!(62,63);
s4 := Sym(64)!(61,62)(63,64);
poly := sub<Sym(64)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s2*s1*s0*s1*s2*s1, 
s3*s4*s3*s4*s3*s4*s3*s4, 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