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Polytope of Type {96}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {96}*192
Also Known As : 96-gon, {96}. if this polytope has another name.
Group : SmallGroup(192,7)
Rank : 2
Schlafli Type : {96}
Number of vertices, edges, etc : 96, 96
Order of s0s1 : 96
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {96,2} of size 384
   {96,4} of size 768
   {96,4} of size 768
   {96,4} of size 768
   {96,4} of size 768
   {96,6} of size 1152
   {96,6} of size 1152
   {96,6} of size 1152
   {96,10} of size 1920
Vertex Figure Of :
   {2,96} of size 384
   {4,96} of size 768
   {4,96} of size 768
   {4,96} of size 768
   {4,96} of size 768
   {6,96} of size 1152
   {6,96} of size 1152
   {6,96} of size 1152
   {10,96} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {48}*96
   3-fold quotients : {32}*64
   4-fold quotients : {24}*48
   6-fold quotients : {16}*32
   8-fold quotients : {12}*24
   12-fold quotients : {8}*16
   16-fold quotients : {6}*12
   24-fold quotients : {4}*8
   32-fold quotients : {3}*6
   48-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   2-fold covers : {192}*384
   3-fold covers : {288}*576
   4-fold covers : {384}*768
   5-fold covers : {480}*960
   6-fold covers : {576}*1152
   7-fold covers : {672}*1344
   9-fold covers : {864}*1728
   10-fold covers : {960}*1920
Permutation Representation (GAP) :
s0 := ( 2, 3)( 5, 6)( 7,10)( 8,12)( 9,11)(13,19)(14,21)(15,20)(16,22)(17,24)
(18,23)(25,37)(26,39)(27,38)(28,40)(29,42)(30,41)(31,46)(32,48)(33,47)(34,43)
(35,45)(36,44)(49,73)(50,75)(51,74)(52,76)(53,78)(54,77)(55,82)(56,84)(57,83)
(58,79)(59,81)(60,80)(61,91)(62,93)(63,92)(64,94)(65,96)(66,95)(67,85)(68,87)
(69,86)(70,88)(71,90)(72,89);;
s1 := ( 1,50)( 2,49)( 3,51)( 4,53)( 5,52)( 6,54)( 7,59)( 8,58)( 9,60)(10,56)
(11,55)(12,57)(13,68)(14,67)(15,69)(16,71)(17,70)(18,72)(19,62)(20,61)(21,63)
(22,65)(23,64)(24,66)(25,86)(26,85)(27,87)(28,89)(29,88)(30,90)(31,95)(32,94)
(33,96)(34,92)(35,91)(36,93)(37,74)(38,73)(39,75)(40,77)(41,76)(42,78)(43,83)
(44,82)(45,84)(46,80)(47,79)(48,81);;
poly := Group([s0,s1]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1");;
s0 := F.1;;  s1 := F.2;;  
rels := [ s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(96)!( 2, 3)( 5, 6)( 7,10)( 8,12)( 9,11)(13,19)(14,21)(15,20)(16,22)
(17,24)(18,23)(25,37)(26,39)(27,38)(28,40)(29,42)(30,41)(31,46)(32,48)(33,47)
(34,43)(35,45)(36,44)(49,73)(50,75)(51,74)(52,76)(53,78)(54,77)(55,82)(56,84)
(57,83)(58,79)(59,81)(60,80)(61,91)(62,93)(63,92)(64,94)(65,96)(66,95)(67,85)
(68,87)(69,86)(70,88)(71,90)(72,89);
s1 := Sym(96)!( 1,50)( 2,49)( 3,51)( 4,53)( 5,52)( 6,54)( 7,59)( 8,58)( 9,60)
(10,56)(11,55)(12,57)(13,68)(14,67)(15,69)(16,71)(17,70)(18,72)(19,62)(20,61)
(21,63)(22,65)(23,64)(24,66)(25,86)(26,85)(27,87)(28,89)(29,88)(30,90)(31,95)
(32,94)(33,96)(34,92)(35,91)(36,93)(37,74)(38,73)(39,75)(40,77)(41,76)(42,78)
(43,83)(44,82)(45,84)(46,80)(47,79)(48,81);
poly := sub<Sym(96)|s0,s1>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
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