Polytope of Type {2,3,6,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,6,8}*768
if this polytope has a name.
Group : SmallGroup(768,1089270)
Rank : 5
Schlafli Type : {2,3,6,8}
Number of vertices, edges, etc : 2, 4, 12, 32, 8
Order of s₀s₁s₂s₃s₄ : 8
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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 : {2,3,6,4}*384
   4-fold quotients : {2,3,6,2}*192
   8-fold quotients : {2,3,3,2}*96
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)
(27,31)(28,32)(29,34)(30,33)(37,38)(39,43)(40,44)(41,46)(42,45)(49,50)(51,55)
(52,56)(53,58)(54,57)(61,62)(63,67)(64,68)(65,70)(66,69)(73,74)(75,79)(76,80)
(77,82)(78,81)(85,86)(87,91)(88,92)(89,94)(90,93)(97,98);;
s3 := ( 3, 6)( 7,14)( 8,12)( 9,13)(10,11)(15,18)(19,26)(20,24)(21,25)(22,23)
(27,42)(28,40)(29,41)(30,39)(31,50)(32,48)(33,49)(34,47)(35,46)(36,44)(37,45)
(38,43)(51,78)(52,76)(53,77)(54,75)(55,86)(56,84)(57,85)(58,83)(59,82)(60,80)
(61,81)(62,79)(63,90)(64,88)(65,89)(66,87)(67,98)(68,96)(69,97)(70,95)(71,94)
(72,92)(73,93)(74,91);;
s4 := ( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,58)(11,59)(12,60)
(13,61)(14,62)(15,63)(16,64)(17,65)(18,66)(19,67)(20,68)(21,69)(22,70)(23,71)
(24,72)(25,73)(26,74)(27,87)(28,88)(29,89)(30,90)(31,91)(32,92)(33,93)(34,94)
(35,95)(36,96)(37,97)(38,98)(39,75)(40,76)(41,77)(42,78)(43,79)(44,80)(45,81)
(46,82)(47,83)(48,84)(49,85)(50,86);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s1*s2*s1*s2*s1*s2, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
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)(27,31)(28,32)(29,34)(30,33)(37,38)(39,43)(40,44)(41,46)(42,45)(49,50)
(51,55)(52,56)(53,58)(54,57)(61,62)(63,67)(64,68)(65,70)(66,69)(73,74)(75,79)
(76,80)(77,82)(78,81)(85,86)(87,91)(88,92)(89,94)(90,93)(97,98);
s3 := Sym(98)!( 3, 6)( 7,14)( 8,12)( 9,13)(10,11)(15,18)(19,26)(20,24)(21,25)
(22,23)(27,42)(28,40)(29,41)(30,39)(31,50)(32,48)(33,49)(34,47)(35,46)(36,44)
(37,45)(38,43)(51,78)(52,76)(53,77)(54,75)(55,86)(56,84)(57,85)(58,83)(59,82)
(60,80)(61,81)(62,79)(63,90)(64,88)(65,89)(66,87)(67,98)(68,96)(69,97)(70,95)
(71,94)(72,92)(73,93)(74,91);
s4 := Sym(98)!( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,58)(11,59)
(12,60)(13,61)(14,62)(15,63)(16,64)(17,65)(18,66)(19,67)(20,68)(21,69)(22,70)
(23,71)(24,72)(25,73)(26,74)(27,87)(28,88)(29,89)(30,90)(31,91)(32,92)(33,93)
(34,94)(35,95)(36,96)(37,97)(38,98)(39,75)(40,76)(41,77)(42,78)(43,79)(44,80)
(45,81)(46,82)(47,83)(48,84)(49,85)(50,86);
poly := sub<Sym(98)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope