Polytope of Type {2,6,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,20}*720
if this polytope has a name.
Group : SmallGroup(720,810)
Rank : 4
Schlafli Type : {2,6,20}
Number of vertices, edges, etc : 2, 9, 90, 30
Order of s₀s₁s₂s₃ : 20
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,20,2} of size 1440
Vertex Figure Of :
   {2,2,6,20} of size 1440
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {2,6,4}*144
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,6,20}*1440
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope