Polytope of Type {6,8,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,8,2}*768g
if this polytope has a name.
Group : SmallGroup(768,1089270)
Rank : 4
Schlafli Type : {6,8,2}
Number of vertices, edges, etc : 24, 96, 32, 2
Order of s₀s₁s₂s₃ : 24
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 : {6,4,2}*384b
   4-fold quotients : {6,8,2}*192, {6,4,2}*192
   8-fold quotients : {6,4,2}*96a, {3,4,2}*96, {6,4,2}*96b, {6,4,2}*96c
   12-fold quotients : {2,8,2}*64
   16-fold quotients : {3,4,2}*48, {6,2,2}*48
   24-fold quotients : {2,4,2}*32
   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 := ( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,21)(18,23)(19,22)(20,24)
(26,27)(29,33)(30,35)(31,34)(32,36)(38,39)(41,45)(42,47)(43,46)(44,48)(50,51)
(53,57)(54,59)(55,58)(56,60)(62,63)(65,69)(66,71)(67,70)(68,72)(74,75)(77,81)
(78,83)(79,82)(80,84)(86,87)(89,93)(90,95)(91,94)(92,96);;
s1 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)(11,12)(13,17)(14,18)(15,20)(16,19)(23,24)
(25,41)(26,42)(27,44)(28,43)(29,37)(30,38)(31,40)(32,39)(33,45)(34,46)(35,48)
(36,47)(49,77)(50,78)(51,80)(52,79)(53,73)(54,74)(55,76)(56,75)(57,81)(58,82)
(59,84)(60,83)(61,89)(62,90)(63,92)(64,91)(65,85)(66,86)(67,88)(68,87)(69,93)
(70,94)(71,96)(72,95);;
s2 := ( 1,52)( 2,51)( 3,50)( 4,49)( 5,56)( 6,55)( 7,54)( 8,53)( 9,60)(10,59)
(11,58)(12,57)(13,64)(14,63)(15,62)(16,61)(17,68)(18,67)(19,66)(20,65)(21,72)
(22,71)(23,70)(24,69)(25,88)(26,87)(27,86)(28,85)(29,92)(30,91)(31,90)(32,89)
(33,96)(34,95)(35,94)(36,93)(37,76)(38,75)(39,74)(40,73)(41,80)(42,79)(43,78)
(44,77)(45,84)(46,83)(47,82)(48,81);;
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, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope