Polytope of Type {40,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40,4}*1920d
if this polytope has a name.
Group : SmallGroup(1920,240864)
Rank : 3
Schlafli Type : {40,4}
Number of vertices, edges, etc : 240, 480, 24
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {20,4}*960d
   4-fold quotients : {10,4}*480c
   8-fold quotients : {5,4}*240, {10,4}*240a, {10,4}*240b
   16-fold quotients : {5,4}*120
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope