Polytope of Type {2,20,3,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,20,3,2}*1920
if this polytope has a name.
Group : SmallGroup(1920,240988)
Rank : 5
Schlafli Type : {2,20,3,2}
Number of vertices, edges, etc : 2, 80, 120, 12, 2
Order of s₀s₁s₂s₃s₄ : 20
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 : {2,10,3,2}*960
   4-fold quotients : {2,5,3,2}*480, {2,10,3,2}*480a, {2,10,3,2}*480b
   8-fold quotients : {2,5,3,2}*240
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4,12)( 5,14)( 6,19)( 7,21)( 9,40)(13,30)(15,46)(16,45)(17,36)(22,25)
(23,38)(24,39)(26,28)(31,35)(32,33)(34,37)(41,49)(42,48)(43,47)(44,50);;
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 := ( 3,11)( 4,21)( 5,15)( 6,26)( 7,12)( 8,29)( 9,39)(10,20)(13,31)(14,46)
(16,32)(17,37)(18,27)(19,28)(22,44)(23,47)(24,40)(25,50)(30,35)(33,45)(34,36)
(38,43)(41,48)(42,49);;
s4 := (51,52);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, 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*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope