Polytope of Type {4,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6}*1920
if this polytope has a name.
Group : SmallGroup(1920,240864)
Rank : 3
Schlafli Type : {4,6}
Number of vertices, edges, etc : 160, 480, 240
Order of s₀s₁s₂ : 40
Order of s₀s₁s₂s₁ : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Halving Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,6}*960
   4-fold quotients : {4,6}*480
   8-fold quotients : {4,6}*240a, {4,6}*240b, {4,6}*240c
   16-fold quotients : {4,6}*120
   120-fold quotients : {4,2}*16
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 1,76)( 2,87)( 3,57)( 4,91)( 5,92)( 6,77)( 7,94)( 8,53)( 9,88)(10,70)
(11,54)(12,62)(13,50)(14,93)(15,52)(16,75)(17,55)(18,60)(19,86)(20,84)(21,72)
(22,58)(23,49)(24,69)(25,59)(26,96)(27,64)(28,89)(29,73)(30,65)(31,61)(32,63)
(33,74)(34,67)(35,82)(36,68)(37,51)(38,83)(39,79)(40,85)(41,71)(42,81)(43,80)
(44,95)(45,66)(46,78)(47,56)(48,90);;
s1 := ( 1,49)( 2,50)( 3,64)( 4,52)( 5,53)( 6,54)( 7,55)( 8,72)( 9,57)(10,74)
(11,58)(12,68)(13,75)(14,62)(15,84)(16,86)(17,69)(18,60)(19,87)(20,67)(21,81)
(22,90)(23,70)(24,96)(25,59)(26,94)(27,82)(28,78)(29,95)(30,65)(31,61)(32,63)
(33,76)(34,91)(35,88)(36,83)(37,51)(38,93)(39,66)(40,80)(41,71)(42,92)(43,79)
(44,89)(45,85)(46,73)(47,56)(48,77);;
s2 := ( 1,18)( 2,25)( 3,21)( 4,30)( 5,31)( 6,32)( 7,37)( 8,20)( 9,41)(10,15)
(11,27)(12,22)(13,24)(14,47)(16,23)(17,36)(19,28)(26,39)(29,35)(33,43)(34,44)
(38,46)(40,42)(45,48)(49,75)(50,69)(51,94)(52,70)(53,84)(54,64)(55,68)(56,93)
(57,72)(58,62)(59,87)(60,76)(61,92)(63,77)(65,91)(66,90)(67,95)(71,88)(73,82)
(74,80)(78,83)(79,96)(81,85)(86,89);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(96)!( 1,76)( 2,87)( 3,57)( 4,91)( 5,92)( 6,77)( 7,94)( 8,53)( 9,88)
(10,70)(11,54)(12,62)(13,50)(14,93)(15,52)(16,75)(17,55)(18,60)(19,86)(20,84)
(21,72)(22,58)(23,49)(24,69)(25,59)(26,96)(27,64)(28,89)(29,73)(30,65)(31,61)
(32,63)(33,74)(34,67)(35,82)(36,68)(37,51)(38,83)(39,79)(40,85)(41,71)(42,81)
(43,80)(44,95)(45,66)(46,78)(47,56)(48,90);
s1 := Sym(96)!( 1,49)( 2,50)( 3,64)( 4,52)( 5,53)( 6,54)( 7,55)( 8,72)( 9,57)
(10,74)(11,58)(12,68)(13,75)(14,62)(15,84)(16,86)(17,69)(18,60)(19,87)(20,67)
(21,81)(22,90)(23,70)(24,96)(25,59)(26,94)(27,82)(28,78)(29,95)(30,65)(31,61)
(32,63)(33,76)(34,91)(35,88)(36,83)(37,51)(38,93)(39,66)(40,80)(41,71)(42,92)
(43,79)(44,89)(45,85)(46,73)(47,56)(48,77);
s2 := Sym(96)!( 1,18)( 2,25)( 3,21)( 4,30)( 5,31)( 6,32)( 7,37)( 8,20)( 9,41)
(10,15)(11,27)(12,22)(13,24)(14,47)(16,23)(17,36)(19,28)(26,39)(29,35)(33,43)
(34,44)(38,46)(40,42)(45,48)(49,75)(50,69)(51,94)(52,70)(53,84)(54,64)(55,68)
(56,93)(57,72)(58,62)(59,87)(60,76)(61,92)(63,77)(65,91)(66,90)(67,95)(71,88)
(73,82)(74,80)(78,83)(79,96)(81,85)(86,89);
poly := sub<Sym(96)|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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 >;

References : None.
to this polytope