Polytope of Type {15,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,8}*1440
if this polytope has a name.
Group : SmallGroup(1440,4612)
Rank : 3
Schlafli Type : {15,8}
Number of vertices, edges, etc : 90, 360, 48
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {15,4}*720
   3-fold quotients : {5,8}*480
   6-fold quotients : {5,4}*240
   12-fold quotients : {5,4}*120
   120-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope