Polytope of Type {2,6,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,8}*768d
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 : {2,6,8}*384a
   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 := ( 3,19)( 4,21)( 5,20)( 6,22)( 7,26)( 8,24)( 9,25)(10,23)(11,34)(12,32)
(13,33)(14,31)(15,30)(16,28)(17,29)(18,27)(36,37)(39,42)(43,50)(44,48)(45,49)
(46,47)(51,67)(52,69)(53,68)(54,70)(55,74)(56,72)(57,73)(58,71)(59,82)(60,80)
(61,81)(62,79)(63,78)(64,76)(65,77)(66,75)(84,85)(87,90)(91,98)(92,96)(93,97)
(94,95);;
s3 := ( 3,63)( 4,64)( 5,65)( 6,66)( 7,59)( 8,60)( 9,61)(10,62)(11,55)(12,56)
(13,57)(14,58)(15,51)(16,52)(17,53)(18,54)(19,79)(20,80)(21,81)(22,82)(23,75)
(24,76)(25,77)(26,78)(27,71)(28,72)(29,73)(30,74)(31,67)(32,68)(33,69)(34,70)
(35,95)(36,96)(37,97)(38,98)(39,91)(40,92)(41,93)(42,94)(43,87)(44,88)(45,89)
(46,90)(47,83)(48,84)(49,85)(50,86);;
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, 
s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
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)!( 3,19)( 4,21)( 5,20)( 6,22)( 7,26)( 8,24)( 9,25)(10,23)(11,34)
(12,32)(13,33)(14,31)(15,30)(16,28)(17,29)(18,27)(36,37)(39,42)(43,50)(44,48)
(45,49)(46,47)(51,67)(52,69)(53,68)(54,70)(55,74)(56,72)(57,73)(58,71)(59,82)
(60,80)(61,81)(62,79)(63,78)(64,76)(65,77)(66,75)(84,85)(87,90)(91,98)(92,96)
(93,97)(94,95);
s3 := Sym(98)!( 3,63)( 4,64)( 5,65)( 6,66)( 7,59)( 8,60)( 9,61)(10,62)(11,55)
(12,56)(13,57)(14,58)(15,51)(16,52)(17,53)(18,54)(19,79)(20,80)(21,81)(22,82)
(23,75)(24,76)(25,77)(26,78)(27,71)(28,72)(29,73)(30,74)(31,67)(32,68)(33,69)
(34,70)(35,95)(36,96)(37,97)(38,98)(39,91)(40,92)(41,93)(42,94)(43,87)(44,88)
(45,89)(46,90)(47,83)(48,84)(49,85)(50,86);
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, 
s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope