Polytope of Type {4,6,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,5}*1920
if this polytope has a name.
Group : SmallGroup(1920,240798)
Rank : 4
Schlafli Type : {4,6,5}
Number of vertices, edges, etc : 4, 96, 120, 40
Order of s₀s₁s₂s₃ : 8
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Orientable
   Flat
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 : {2,6,5}*960, {4,6,5}*960a
   4-fold quotients : {4,6,5}*480a, {2,6,5}*480a
   8-fold quotients : {2,6,5}*240a
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 1,45)( 2,46)( 3,48)( 4,47)( 5,55)( 6,56)( 7,61)( 8,62)( 9,65)(10,66)
(11,50)(12,49)(13,69)(14,70)(15,73)(16,74)(17,52)(18,51)(19,77)(20,78)(21,54)
(22,53)(23,79)(24,80)(25,58)(26,57)(27,85)(28,86)(29,60)(30,59)(31,82)(32,81)
(33,64)(34,63)(35,68)(36,67)(37,75)(38,76)(39,87)(40,88)(41,72)(42,71)(43,84)
(44,83);;
s1 := ( 1, 3)( 2, 4)( 7,39)( 8,40)( 9,35)(10,36)(11,12)(13,32)(14,31)(15,29)
(16,30)(17,44)(18,43)(19,34)(20,33)(21,23)(22,24)(25,38)(26,37)(27,41)(28,42)
(45,47)(46,48)(49,50)(51,84)(52,83)(53,80)(54,79)(57,75)(58,76)(59,74)(60,73)
(61,87)(62,88)(63,77)(64,78)(65,68)(66,67)(69,81)(70,82)(71,86)(72,85);;
s2 := ( 1,45)( 2,46)( 3,47)( 4,48)( 5,51)( 6,52)( 7,50)( 8,49)( 9,57)(10,58)
(11,61)(12,62)(13,54)(14,53)(15,81)(16,82)(17,56)(18,55)(19,78)(20,77)(21,69)
(22,70)(23,86)(24,85)(25,66)(26,65)(27,80)(28,79)(29,75)(30,76)(31,74)(32,73)
(33,63)(34,64)(35,71)(36,72)(37,60)(38,59)(39,87)(40,88)(41,67)(42,68)(43,84)
(44,83);;
s3 := ( 1,45)( 2,46)( 3,47)( 4,48)( 5,56)( 6,55)( 7,68)( 8,67)( 9,87)(10,88)
(11,49)(12,50)(13,81)(14,82)(15,73)(16,74)(17,80)(18,79)(19,71)(20,72)(21,84)
(22,83)(23,51)(24,52)(25,75)(26,76)(27,64)(28,63)(29,60)(30,59)(31,70)(32,69)
(33,85)(34,86)(35,61)(36,62)(37,58)(38,57)(39,65)(40,66)(41,78)(42,77)(43,54)
(44,53);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s1*s2*s3*s2*s1*s3*s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(88)!( 1,45)( 2,46)( 3,48)( 4,47)( 5,55)( 6,56)( 7,61)( 8,62)( 9,65)
(10,66)(11,50)(12,49)(13,69)(14,70)(15,73)(16,74)(17,52)(18,51)(19,77)(20,78)
(21,54)(22,53)(23,79)(24,80)(25,58)(26,57)(27,85)(28,86)(29,60)(30,59)(31,82)
(32,81)(33,64)(34,63)(35,68)(36,67)(37,75)(38,76)(39,87)(40,88)(41,72)(42,71)
(43,84)(44,83);
s1 := Sym(88)!( 1, 3)( 2, 4)( 7,39)( 8,40)( 9,35)(10,36)(11,12)(13,32)(14,31)
(15,29)(16,30)(17,44)(18,43)(19,34)(20,33)(21,23)(22,24)(25,38)(26,37)(27,41)
(28,42)(45,47)(46,48)(49,50)(51,84)(52,83)(53,80)(54,79)(57,75)(58,76)(59,74)
(60,73)(61,87)(62,88)(63,77)(64,78)(65,68)(66,67)(69,81)(70,82)(71,86)(72,85);
s2 := Sym(88)!( 1,45)( 2,46)( 3,47)( 4,48)( 5,51)( 6,52)( 7,50)( 8,49)( 9,57)
(10,58)(11,61)(12,62)(13,54)(14,53)(15,81)(16,82)(17,56)(18,55)(19,78)(20,77)
(21,69)(22,70)(23,86)(24,85)(25,66)(26,65)(27,80)(28,79)(29,75)(30,76)(31,74)
(32,73)(33,63)(34,64)(35,71)(36,72)(37,60)(38,59)(39,87)(40,88)(41,67)(42,68)
(43,84)(44,83);
s3 := Sym(88)!( 1,45)( 2,46)( 3,47)( 4,48)( 5,56)( 6,55)( 7,68)( 8,67)( 9,87)
(10,88)(11,49)(12,50)(13,81)(14,82)(15,73)(16,74)(17,80)(18,79)(19,71)(20,72)
(21,84)(22,83)(23,51)(24,52)(25,75)(26,76)(27,64)(28,63)(29,60)(30,59)(31,70)
(32,69)(33,85)(34,86)(35,61)(36,62)(37,58)(38,57)(39,65)(40,66)(41,78)(42,77)
(43,54)(44,53);
poly := sub<Sym(88)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s1*s2*s3*s2*s1*s3*s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s1 >;

References : None.
to this polytope