Polytope of Type {4,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,20}*960a
if this polytope has a name.
Group : SmallGroup(960,5719)
Rank : 3
Schlafli Type : {4,20}
Number of vertices, edges, etc : 24, 240, 120
Order of s₀s₁s₂ : 24
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,20,2} of size 1920
Vertex Figure Of :
   {2,4,20} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,10}*480b
   4-fold quotients : {4,10}*240b
   8-fold quotients : {4,5}*120
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,20}*1920b
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1 >;

References : None.
to this polytope