Polytope of Type {2,20,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,20,6}*1920e
if this polytope has a name.
Group : SmallGroup(1920,240988)
Rank : 4
Schlafli Type : {2,20,6}
Number of vertices, edges, etc : 2, 80, 240, 24
Order of s₀s₁s₂s₃ : 20
Order of s₀s₁s₂s₃s₂s₁ : 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 : {2,20,3}*960, {2,10,6}*960c
   4-fold quotients : {2,5,6}*480b, {2,10,3}*480, {2,10,6}*480c, {2,10,6}*480d, {2,10,6}*480e, {2,10,6}*480f
   8-fold quotients : {2,5,3}*240, {2,5,6}*240b, {2,5,6}*240c, {2,10,3}*240a, {2,10,3}*240b
   16-fold quotients : {2,5,3}*120
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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