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Polytope of Type {8,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,6}*384e
if this polytope has a name.
Group : SmallGroup(384,17949)
Rank : 3
Schlafli Type : {8,6}
Number of vertices, edges, etc : 32, 96, 24
Order of s0s1s2 : 6
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {8,6,2} of size 768
Vertex Figure Of :
   {2,8,6} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {8,3}*192
   4-fold quotients : {4,6}*96
   8-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
   16-fold quotients : {4,3}*24, {2,6}*24
   32-fold quotients : {2,3}*12
   48-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,6}*768d, {8,12}*768l, {8,6}*768h, {8,12}*768n, {8,12}*768q, {8,6}*768k, {8,12}*768x
   3-fold covers : {8,18}*1152d, {24,6}*1152c, {24,6}*1152e
   5-fold covers : {40,6}*1920c, {8,30}*1920d
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 := ( 1,89)( 2,92)( 3,91)( 4,90)( 5,87)( 6,86)( 7,85)( 8,88)( 9,81)(10,84)
(11,83)(12,82)(13,93)(14,96)(15,95)(16,94)(17,73)(18,76)(19,75)(20,74)(21,71)
(22,70)(23,69)(24,72)(25,65)(26,68)(27,67)(28,66)(29,77)(30,80)(31,79)(32,78)
(33,57)(34,60)(35,59)(36,58)(37,55)(38,54)(39,53)(40,56)(41,49)(42,52)(43,51)
(44,50)(45,61)(46,64)(47,63)(48,62);;
poly := Group([s0,s1,s2]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s2*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(96)!( 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(96)!( 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(96)!( 1,89)( 2,92)( 3,91)( 4,90)( 5,87)( 6,86)( 7,85)( 8,88)( 9,81)
(10,84)(11,83)(12,82)(13,93)(14,96)(15,95)(16,94)(17,73)(18,76)(19,75)(20,74)
(21,71)(22,70)(23,69)(24,72)(25,65)(26,68)(27,67)(28,66)(29,77)(30,80)(31,79)
(32,78)(33,57)(34,60)(35,59)(36,58)(37,55)(38,54)(39,53)(40,56)(41,49)(42,52)
(43,51)(44,50)(45,61)(46,64)(47,63)(48,62);
poly := sub<Sym(96)|s0,s1,s2>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s2*s1 >; 
 
References : None.
to this polytope