Polytope of Type {4,40}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,40}*1920c
if this polytope has a name.
Group : SmallGroup(1920,240857)
Rank : 3
Schlafli Type : {4,40}
Number of vertices, edges, etc : 24, 480, 240
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {4,20}*960d
   4-fold quotients : {4,10}*480c
   8-fold quotients : {4,5}*240, {4,10}*240a, {4,10}*240b
   16-fold quotients : {4,5}*120
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
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