Polytope of Type {20,4}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope