Polytope of Type {2,6,8}

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

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

Permutation Representation (Magma) :

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

to this polytope