Polytope of Type {5,8,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,8,4}*1920
if this polytope has a name.
Group : SmallGroup(1920,240798)
Rank : 4
Schlafli Type : {5,8,4}
Number of vertices, edges, etc : 30, 120, 96, 4
Order of s₀s₁s₂s₃ : 12
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 : {5,8,2}*960, {5,4,4}*960
   4-fold quotients : {5,4,4}*480, {5,4,2}*480
   8-fold quotients : {5,4,2}*240
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope