Polytope of Type {6,15}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,15}*960
if this polytope has a name.
Group : SmallGroup(960,5762)
Rank : 3
Schlafli Type : {6,15}
Number of vertices, edges, etc : 32, 240, 80
Order of s₀s₁s₂ : 40
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,15,2} of size 1920
Vertex Figure Of :
   {2,6,15} of size 1920
Quotients (Maximal Quotients in Boldface) :
   4-fold quotients : {6,15}*240
   5-fold quotients : {6,3}*192
   20-fold quotients : {6,3}*48
   40-fold quotients : {3,3}*24
   48-fold quotients : {2,5}*20
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,15}*1920, {6,30}*1920a
Permutation Representation (GAP) :

s0 := ( 3, 4)( 5,10)( 6, 9)( 7,11)( 8,12)(15,16)(19,20)(21,26)(22,25)(23,27)
(24,28)(31,32)(35,36)(37,42)(38,41)(39,43)(40,44)(47,48)(51,52)(53,58)(54,57)
(55,59)(56,60)(63,64)(67,68)(69,74)(70,73)(71,75)(72,76)(79,80);;
s1 := ( 2, 3)( 5, 8)( 9,16)(10,14)(11,15)(12,13)(17,65)(18,67)(19,66)(20,68)
(21,72)(22,70)(23,71)(24,69)(25,80)(26,78)(27,79)(28,77)(29,76)(30,74)(31,75)
(32,73)(33,49)(34,51)(35,50)(36,52)(37,56)(38,54)(39,55)(40,53)(41,64)(42,62)
(43,63)(44,61)(45,60)(46,58)(47,59)(48,57);;
s2 := ( 1,29)( 2,30)( 3,32)( 4,31)( 5,22)( 6,21)( 7,23)( 8,24)( 9,26)(10,25)
(11,27)(12,28)(13,17)(14,18)(15,20)(16,19)(33,77)(34,78)(35,80)(36,79)(37,70)
(38,69)(39,71)(40,72)(41,74)(42,73)(43,75)(44,76)(45,65)(46,66)(47,68)(48,67)
(49,61)(50,62)(51,64)(52,63)(53,54)(57,58);;
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*s0*s1*s2*s1*s2*s1, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(80)!( 3, 4)( 5,10)( 6, 9)( 7,11)( 8,12)(15,16)(19,20)(21,26)(22,25)
(23,27)(24,28)(31,32)(35,36)(37,42)(38,41)(39,43)(40,44)(47,48)(51,52)(53,58)
(54,57)(55,59)(56,60)(63,64)(67,68)(69,74)(70,73)(71,75)(72,76)(79,80);
s1 := Sym(80)!( 2, 3)( 5, 8)( 9,16)(10,14)(11,15)(12,13)(17,65)(18,67)(19,66)
(20,68)(21,72)(22,70)(23,71)(24,69)(25,80)(26,78)(27,79)(28,77)(29,76)(30,74)
(31,75)(32,73)(33,49)(34,51)(35,50)(36,52)(37,56)(38,54)(39,55)(40,53)(41,64)
(42,62)(43,63)(44,61)(45,60)(46,58)(47,59)(48,57);
s2 := Sym(80)!( 1,29)( 2,30)( 3,32)( 4,31)( 5,22)( 6,21)( 7,23)( 8,24)( 9,26)
(10,25)(11,27)(12,28)(13,17)(14,18)(15,20)(16,19)(33,77)(34,78)(35,80)(36,79)
(37,70)(38,69)(39,71)(40,72)(41,74)(42,73)(43,75)(44,76)(45,65)(46,66)(47,68)
(48,67)(49,61)(50,62)(51,64)(52,63)(53,54)(57,58);
poly := sub<Sym(80)|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*s0*s1*s2*s1*s2*s1, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;

References : None.
to this polytope