Polytope of Type {6,8,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,8,2}*768e
if this polytope has a name.
Group : SmallGroup(768,1089093)
Rank : 4
Schlafli Type : {6,8,2}
Number of vertices, edges, etc : 24, 96, 32, 2
Order of s₀s₁s₂s₃ : 6
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 : {3,8,2}*384
   4-fold quotients : {6,4,2}*192
   8-fold quotients : {3,4,2}*96, {6,4,2}*96b, {6,4,2}*96c
   16-fold quotients : {3,4,2}*48, {6,2,2}*48
   32-fold quotients : {3,2,2}*24
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope