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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,6,20}*1920a
if this polytope has a name.
Group : SmallGroup(1920,208127)
Rank : 5
Schlafli Type : {4,2,6,20}
Number of vertices, edges, etc : 4, 4, 6, 60, 20
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 : {2,2,6,20}*960a, {4,2,6,10}*960
   3-fold quotients : {4,2,2,20}*640
   4-fold quotients : {2,2,6,10}*480
   5-fold quotients : {4,2,6,4}*384a
   6-fold quotients : {2,2,2,20}*320, {4,2,2,10}*320
   10-fold quotients : {2,2,6,4}*192a, {4,2,6,2}*192
   12-fold quotients : {4,2,2,5}*160, {2,2,2,10}*160
   15-fold quotients : {4,2,2,4}*128
   20-fold quotients : {4,2,3,2}*96, {2,2,6,2}*96
   24-fold quotients : {2,2,2,5}*80
   30-fold quotients : {2,2,2,4}*64, {4,2,2,2}*64
   40-fold quotients : {2,2,3,2}*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 := (10,15)(11,16)(12,17)(13,18)(14,19)(25,30)(26,31)(27,32)(28,33)(29,34)
(40,45)(41,46)(42,47)(43,48)(44,49)(55,60)(56,61)(57,62)(58,63)(59,64);;
s3 := ( 5,10)( 6,14)( 7,13)( 8,12)( 9,11)(16,19)(17,18)(20,25)(21,29)(22,28)
(23,27)(24,26)(31,34)(32,33)(35,55)(36,59)(37,58)(38,57)(39,56)(40,50)(41,54)
(42,53)(43,52)(44,51)(45,60)(46,64)(47,63)(48,62)(49,61);;
s4 := ( 5,36)( 6,35)( 7,39)( 8,38)( 9,37)(10,41)(11,40)(12,44)(13,43)(14,42)
(15,46)(16,45)(17,49)(18,48)(19,47)(20,51)(21,50)(22,54)(23,53)(24,52)(25,56)
(26,55)(27,59)(28,58)(29,57)(30,61)(31,60)(32,64)(33,63)(34,62);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope