Polytope of Type {2,8,6}

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

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

Permutation Representation (Magma) :

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

to this polytope