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Polytope of Type {8,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,6,2}*768d
if this polytope has a name.
Group : SmallGroup(768,1089093)
Rank : 4
Schlafli Type : {8,6,2}
Number of vertices, edges, etc : 32, 96, 24, 2
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 : {8,6,2}*384a
   4-fold quotients : {4,6,2}*192
   8-fold quotients : {4,3,2}*96, {4,6,2}*96b, {4,6,2}*96c
   16-fold quotients : {4,3,2}*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, 9)( 2,10)( 3,11)( 4,12)( 5,16)( 6,15)( 7,14)( 8,13)(17,25)(18,26)
(19,27)(20,28)(21,32)(22,31)(23,30)(24,29)(33,41)(34,42)(35,43)(36,44)(37,48)
(38,47)(39,46)(40,45)(49,57)(50,58)(51,59)(52,60)(53,64)(54,63)(55,62)(56,61)
(65,73)(66,74)(67,75)(68,76)(69,80)(70,79)(71,78)(72,77)(81,89)(82,90)(83,91)
(84,92)(85,96)(86,95)(87,94)(88,93);;
s1 := ( 3, 4)( 5,10)( 6, 9)( 7,11)( 8,12)(15,16)(17,33)(18,34)(19,36)(20,35)
(21,42)(22,41)(23,43)(24,44)(25,38)(26,37)(27,39)(28,40)(29,45)(30,46)(31,48)
(32,47)(51,52)(53,58)(54,57)(55,59)(56,60)(63,64)(65,81)(66,82)(67,84)(68,83)
(69,90)(70,89)(71,91)(72,92)(73,86)(74,85)(75,87)(76,88)(77,93)(78,94)(79,96)
(80,95);;
s2 := ( 1,81)( 2,84)( 3,83)( 4,82)( 5,94)( 6,95)( 7,96)( 8,93)( 9,89)(10,92)
(11,91)(12,90)(13,88)(14,85)(15,86)(16,87)(17,65)(18,68)(19,67)(20,66)(21,78)
(22,79)(23,80)(24,77)(25,73)(26,76)(27,75)(28,74)(29,72)(30,69)(31,70)(32,71)
(33,49)(34,52)(35,51)(36,50)(37,62)(38,63)(39,64)(40,61)(41,57)(42,60)(43,59)
(44,58)(45,56)(46,53)(47,54)(48,55);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(98)!( 1, 9)( 2,10)( 3,11)( 4,12)( 5,16)( 6,15)( 7,14)( 8,13)(17,25)
(18,26)(19,27)(20,28)(21,32)(22,31)(23,30)(24,29)(33,41)(34,42)(35,43)(36,44)
(37,48)(38,47)(39,46)(40,45)(49,57)(50,58)(51,59)(52,60)(53,64)(54,63)(55,62)
(56,61)(65,73)(66,74)(67,75)(68,76)(69,80)(70,79)(71,78)(72,77)(81,89)(82,90)
(83,91)(84,92)(85,96)(86,95)(87,94)(88,93);
s1 := Sym(98)!( 3, 4)( 5,10)( 6, 9)( 7,11)( 8,12)(15,16)(17,33)(18,34)(19,36)
(20,35)(21,42)(22,41)(23,43)(24,44)(25,38)(26,37)(27,39)(28,40)(29,45)(30,46)
(31,48)(32,47)(51,52)(53,58)(54,57)(55,59)(56,60)(63,64)(65,81)(66,82)(67,84)
(68,83)(69,90)(70,89)(71,91)(72,92)(73,86)(74,85)(75,87)(76,88)(77,93)(78,94)
(79,96)(80,95);
s2 := Sym(98)!( 1,81)( 2,84)( 3,83)( 4,82)( 5,94)( 6,95)( 7,96)( 8,93)( 9,89)
(10,92)(11,91)(12,90)(13,88)(14,85)(15,86)(16,87)(17,65)(18,68)(19,67)(20,66)
(21,78)(22,79)(23,80)(24,77)(25,73)(26,76)(27,75)(28,74)(29,72)(30,69)(31,70)
(32,71)(33,49)(34,52)(35,51)(36,50)(37,62)(38,63)(39,64)(40,61)(41,57)(42,60)
(43,59)(44,58)(45,56)(46,53)(47,54)(48,55);
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

to this polytope