Polytope of Type {10,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,4}*1920
if this polytope has a name.
Group : SmallGroup(1920,240816)
Rank : 3
Schlafli Type : {10,4}
Number of vertices, edges, etc : 240, 480, 96
Order of s₀s₁s₂ : 24
Order of s₀s₁s₂s₁ : 6
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 : {10,4}*960
   4-fold quotients : {10,4}*480a, {10,4}*480b, {10,4}*480c
   8-fold quotients : {5,4}*240, {10,4}*240a, {10,4}*240b
   16-fold quotients : {5,4}*120
   120-fold quotients : {2,4}*16
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope