Polytope of Type {2,8,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,6}*768f
if this polytope has a name.
Group : SmallGroup(768,1089251)
Rank : 4
Schlafli Type : {2,8,6}
Number of vertices, edges, etc : 2, 32, 96, 24
Order of s₀s₁s₂s₃ : 12
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 : {2,4,6}*384b, {2,8,6}*384b, {2,8,6}*384c
   4-fold quotients : {2,8,3}*192, {2,4,6}*192
   8-fold quotients : {2,4,6}*96a, {2,4,3}*96, {2,4,6}*96b, {2,4,6}*96c
   16-fold quotients : {2,4,3}*48, {2,2,6}*48
   24-fold quotients : {2,4,2}*32
   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 := ( 3,55)( 4,56)( 5,58)( 6,57)( 7,52)( 8,51)( 9,53)(10,54)(11,63)(12,64)
(13,66)(14,65)(15,60)(16,59)(17,61)(18,62)(19,71)(20,72)(21,74)(22,73)(23,68)
(24,67)(25,69)(26,70)(27,79)(28,80)(29,82)(30,81)(31,76)(32,75)(33,77)(34,78)
(35,87)(36,88)(37,90)(38,89)(39,84)(40,83)(41,85)(42,86)(43,95)(44,96)(45,98)
(46,97)(47,92)(48,91)(49,93)(50,94);;
s2 := ( 5, 8)( 6, 7)( 9,10)(11,19)(12,20)(13,24)(14,23)(15,22)(16,21)(17,26)
(18,25)(29,32)(30,31)(33,34)(35,43)(36,44)(37,48)(38,47)(39,46)(40,45)(41,50)
(42,49)(51,76)(52,75)(53,79)(54,80)(55,77)(56,78)(57,81)(58,82)(59,92)(60,91)
(61,95)(62,96)(63,93)(64,94)(65,97)(66,98)(67,84)(68,83)(69,87)(70,88)(71,85)
(72,86)(73,89)(74,90);;
s3 := ( 3,19)( 4,20)( 5,25)( 6,26)( 7,24)( 8,23)( 9,21)(10,22)(13,17)(14,18)
(15,16)(27,43)(28,44)(29,49)(30,50)(31,48)(32,47)(33,45)(34,46)(37,41)(38,42)
(39,40)(51,68)(52,67)(53,74)(54,73)(55,71)(56,72)(57,70)(58,69)(59,60)(61,66)
(62,65)(75,92)(76,91)(77,98)(78,97)(79,95)(80,96)(81,94)(82,93)(83,84)(85,90)
(86,89);;
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, 
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*s1*s2*s3*s2*s1*s2*s1*s2, 
s2*s1*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s1*s3*s2*s1, 
s1*s3*s2*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s3*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope