Polytope of Type {6,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,24}*960c
if this polytope has a name.
Group : SmallGroup(960,5719)
Rank : 3
Schlafli Type : {6,24}
Number of vertices, edges, etc : 20, 240, 80
Order of s₀s₁s₂ : 24
Order of s₀s₁s₂s₁ : 20
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,24,2} of size 1920
Vertex Figure Of :
   {2,6,24} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,12}*480b
   4-fold quotients : {6,6}*240a
   8-fold quotients : {6,6}*120
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,24}*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, 6)( 2,28)( 3,36)( 4,26)( 5,14)( 7,41)( 8,37)( 9,18)(10,11)(12,27)
(13,48)(15,16)(17,25)(19,39)(20,47)(21,34)(22,33)(23,24)(29,43)(30,35)(31,44)
(32,38)(40,42)(45,46);;
s2 := ( 1,16)( 2,32)( 3,13)( 4, 6)( 5, 7)( 8,42)( 9,44)(10,19)(11,24)(12,23)
(14,27)(15,33)(17,35)(18,34)(20,37)(21,40)(22,25)(26,41)(28,30)(29,36)(31,39)
(38,45)(43,47)(46,48);;
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*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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, 6)( 2,28)( 3,36)( 4,26)( 5,14)( 7,41)( 8,37)( 9,18)(10,11)
(12,27)(13,48)(15,16)(17,25)(19,39)(20,47)(21,34)(22,33)(23,24)(29,43)(30,35)
(31,44)(32,38)(40,42)(45,46);
s2 := Sym(48)!( 1,16)( 2,32)( 3,13)( 4, 6)( 5, 7)( 8,42)( 9,44)(10,19)(11,24)
(12,23)(14,27)(15,33)(17,35)(18,34)(20,37)(21,40)(22,25)(26,41)(28,30)(29,36)
(31,39)(38,45)(43,47)(46,48);
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*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1 >;

References : None.
to this polytope