Polytope of Type {6,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,24}*1440a
if this polytope has a name.
Group : SmallGroup(1440,4612)
Rank : 3
Schlafli Type : {6,24}
Number of vertices, edges, etc : 30, 360, 120
Order of s₀s₁s₂ : 30
Order of s₀s₁s₂s₁ : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,12}*720a
   3-fold quotients : {6,8}*480a
   6-fold quotients : {6,4}*240c
   12-fold quotients : {6,4}*120
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope