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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,20,6}*1920a
if this polytope has a name.
Group : SmallGroup(1920,208127)
Rank : 5
Schlafli Type : {4,2,20,6}
Number of vertices, edges, etc : 4, 4, 20, 60, 6
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 : {2,2,20,6}*960a, {4,2,10,6}*960
   3-fold quotients : {4,2,20,2}*640
   4-fold quotients : {2,2,10,6}*480
   5-fold quotients : {4,2,4,6}*384a
   6-fold quotients : {2,2,20,2}*320, {4,2,10,2}*320
   10-fold quotients : {2,2,4,6}*192a, {4,2,2,6}*192
   12-fold quotients : {4,2,5,2}*160, {2,2,10,2}*160
   15-fold quotients : {4,2,4,2}*128
   20-fold quotients : {4,2,2,3}*96, {2,2,2,6}*96
   24-fold quotients : {2,2,5,2}*80
   30-fold quotients : {2,2,4,2}*64, {4,2,2,2}*64
   40-fold quotients : {2,2,2,3}*48
   60-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 6, 9)( 7, 8)(11,14)(12,13)(16,19)(17,18)(21,24)(22,23)(26,29)(27,28)
(31,34)(32,33)(35,50)(36,54)(37,53)(38,52)(39,51)(40,55)(41,59)(42,58)(43,57)
(44,56)(45,60)(46,64)(47,63)(48,62)(49,61);;
s3 := ( 5,36)( 6,35)( 7,39)( 8,38)( 9,37)(10,46)(11,45)(12,49)(13,48)(14,47)
(15,41)(16,40)(17,44)(18,43)(19,42)(20,51)(21,50)(22,54)(23,53)(24,52)(25,61)
(26,60)(27,64)(28,63)(29,62)(30,56)(31,55)(32,59)(33,58)(34,57);;
s4 := ( 5,10)( 6,11)( 7,12)( 8,13)( 9,14)(20,25)(21,26)(22,27)(23,28)(24,29)
(35,40)(36,41)(37,42)(38,43)(39,44)(50,55)(51,56)(52,57)(53,58)(54,59);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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)!(2,3);
s1 := Sym(64)!(1,2)(3,4);
s2 := Sym(64)!( 6, 9)( 7, 8)(11,14)(12,13)(16,19)(17,18)(21,24)(22,23)(26,29)
(27,28)(31,34)(32,33)(35,50)(36,54)(37,53)(38,52)(39,51)(40,55)(41,59)(42,58)
(43,57)(44,56)(45,60)(46,64)(47,63)(48,62)(49,61);
s3 := Sym(64)!( 5,36)( 6,35)( 7,39)( 8,38)( 9,37)(10,46)(11,45)(12,49)(13,48)
(14,47)(15,41)(16,40)(17,44)(18,43)(19,42)(20,51)(21,50)(22,54)(23,53)(24,52)
(25,61)(26,60)(27,64)(28,63)(29,62)(30,56)(31,55)(32,59)(33,58)(34,57);
s4 := Sym(64)!( 5,10)( 6,11)( 7,12)( 8,13)( 9,14)(20,25)(21,26)(22,27)(23,28)
(24,29)(35,40)(36,41)(37,42)(38,43)(39,44)(50,55)(51,56)(52,57)(53,58)(54,59);
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, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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