Polytope of Type {2,6,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,24}*768a
if this polytope has a name.
Group : SmallGroup(768,1089270)
Rank : 4
Schlafli Type : {2,6,24}
Number of vertices, edges, etc : 2, 8, 96, 32
Order of s₀s₁s₂s₃ : 8
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   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 : {2,6,12}*384a
   4-fold quotients : {2,6,6}*192
   8-fold quotients : {2,3,6}*96, {2,6,3}*96
   12-fold quotients : {2,2,8}*64
   16-fold quotients : {2,3,3}*48
   24-fold quotients : {2,2,4}*32
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(16,17)(19,23)(20,25)(21,24)(22,26)
(28,29)(31,35)(32,37)(33,36)(34,38)(40,41)(43,47)(44,49)(45,48)(46,50)(52,53)
(55,59)(56,61)(57,60)(58,62)(64,65)(67,71)(68,73)(69,72)(70,74)(76,77)(79,83)
(80,85)(81,84)(82,86)(88,89)(91,95)(92,97)(93,96)(94,98);;
s2 := ( 3, 7)( 4, 8)( 5,10)( 6, 9)(13,14)(15,19)(16,20)(17,22)(18,21)(25,26)
(27,43)(28,44)(29,46)(30,45)(31,39)(32,40)(33,42)(34,41)(35,47)(36,48)(37,50)
(38,49)(51,79)(52,80)(53,82)(54,81)(55,75)(56,76)(57,78)(58,77)(59,83)(60,84)
(61,86)(62,85)(63,91)(64,92)(65,94)(66,93)(67,87)(68,88)(69,90)(70,89)(71,95)
(72,96)(73,98)(74,97);;
s3 := ( 3,54)( 4,52)( 5,53)( 6,51)( 7,62)( 8,60)( 9,61)(10,59)(11,58)(12,56)
(13,57)(14,55)(15,66)(16,64)(17,65)(18,63)(19,74)(20,72)(21,73)(22,71)(23,70)
(24,68)(25,69)(26,67)(27,90)(28,88)(29,89)(30,87)(31,98)(32,96)(33,97)(34,95)
(35,94)(36,92)(37,93)(38,91)(39,78)(40,76)(41,77)(42,75)(43,86)(44,84)(45,85)
(46,83)(47,82)(48,80)(49,81)(50,79);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(98)!(1,2);
s1 := Sym(98)!( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(16,17)(19,23)(20,25)(21,24)
(22,26)(28,29)(31,35)(32,37)(33,36)(34,38)(40,41)(43,47)(44,49)(45,48)(46,50)
(52,53)(55,59)(56,61)(57,60)(58,62)(64,65)(67,71)(68,73)(69,72)(70,74)(76,77)
(79,83)(80,85)(81,84)(82,86)(88,89)(91,95)(92,97)(93,96)(94,98);
s2 := Sym(98)!( 3, 7)( 4, 8)( 5,10)( 6, 9)(13,14)(15,19)(16,20)(17,22)(18,21)
(25,26)(27,43)(28,44)(29,46)(30,45)(31,39)(32,40)(33,42)(34,41)(35,47)(36,48)
(37,50)(38,49)(51,79)(52,80)(53,82)(54,81)(55,75)(56,76)(57,78)(58,77)(59,83)
(60,84)(61,86)(62,85)(63,91)(64,92)(65,94)(66,93)(67,87)(68,88)(69,90)(70,89)
(71,95)(72,96)(73,98)(74,97);
s3 := Sym(98)!( 3,54)( 4,52)( 5,53)( 6,51)( 7,62)( 8,60)( 9,61)(10,59)(11,58)
(12,56)(13,57)(14,55)(15,66)(16,64)(17,65)(18,63)(19,74)(20,72)(21,73)(22,71)
(23,70)(24,68)(25,69)(26,67)(27,90)(28,88)(29,89)(30,87)(31,98)(32,96)(33,97)
(34,95)(35,94)(36,92)(37,93)(38,91)(39,78)(40,76)(41,77)(42,75)(43,86)(44,84)
(45,85)(46,83)(47,82)(48,80)(49,81)(50,79);
poly := sub<Sym(98)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2 >;

to this polytope