Polytope of Type {24,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,6}*1440b
if this polytope has a name.
Group : SmallGroup(1440,4612)
Rank : 3
Schlafli Type : {24,6}
Number of vertices, edges, etc : 120, 360, 30
Order of s₀s₁s₂ : 15
Order of s₀s₁s₂s₁ : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,6}*720a
   3-fold quotients : {8,6}*480a
   6-fold quotients : {4,6}*240c
   12-fold quotients : {4,6}*120
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope