Polytope of Type {2,20,6}

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

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

Permutation Representation (Magma) :

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

to this polytope