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Polytope of Type {92}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {92}*184
Also Known As : 92-gon, {92}. if this polytope has another name.
Group : SmallGroup(184,5)
Rank : 2
Schlafli Type : {92}
Number of vertices, edges, etc : 92, 92
Order of s0s1 : 92
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {92,2} of size 368
   {92,4} of size 736
   {92,6} of size 1104
   {92,6} of size 1104
   {92,8} of size 1472
   {92,8} of size 1472
   {92,4} of size 1472
   {92,6} of size 1656
   {92,10} of size 1840
Vertex Figure Of :
   {2,92} of size 368
   {4,92} of size 736
   {6,92} of size 1104
   {6,92} of size 1104
   {8,92} of size 1472
   {8,92} of size 1472
   {4,92} of size 1472
   {6,92} of size 1656
   {10,92} of size 1840
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {46}*92
   4-fold quotients : {23}*46
   23-fold quotients : {4}*8
   46-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   2-fold covers : {184}*368
   3-fold covers : {276}*552
   4-fold covers : {368}*736
   5-fold covers : {460}*920
   6-fold covers : {552}*1104
   7-fold covers : {644}*1288
   8-fold covers : {736}*1472
   9-fold covers : {828}*1656
   10-fold covers : {920}*1840
Permutation Representation (GAP) :
s0 := ( 2,23)( 3,22)( 4,21)( 5,20)( 6,19)( 7,18)( 8,17)( 9,16)(10,15)(11,14)
(12,13)(25,46)(26,45)(27,44)(28,43)(29,42)(30,41)(31,40)(32,39)(33,38)(34,37)
(35,36)(47,70)(48,92)(49,91)(50,90)(51,89)(52,88)(53,87)(54,86)(55,85)(56,84)
(57,83)(58,82)(59,81)(60,80)(61,79)(62,78)(63,77)(64,76)(65,75)(66,74)(67,73)
(68,72)(69,71);;
s1 := ( 1,48)( 2,47)( 3,69)( 4,68)( 5,67)( 6,66)( 7,65)( 8,64)( 9,63)(10,62)
(11,61)(12,60)(13,59)(14,58)(15,57)(16,56)(17,55)(18,54)(19,53)(20,52)(21,51)
(22,50)(23,49)(24,71)(25,70)(26,92)(27,91)(28,90)(29,89)(30,88)(31,87)(32,86)
(33,85)(34,84)(35,83)(36,82)(37,81)(38,80)(39,79)(40,78)(41,77)(42,76)(43,75)
(44,74)(45,73)(46,72);;
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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(92)!( 2,23)( 3,22)( 4,21)( 5,20)( 6,19)( 7,18)( 8,17)( 9,16)(10,15)
(11,14)(12,13)(25,46)(26,45)(27,44)(28,43)(29,42)(30,41)(31,40)(32,39)(33,38)
(34,37)(35,36)(47,70)(48,92)(49,91)(50,90)(51,89)(52,88)(53,87)(54,86)(55,85)
(56,84)(57,83)(58,82)(59,81)(60,80)(61,79)(62,78)(63,77)(64,76)(65,75)(66,74)
(67,73)(68,72)(69,71);
s1 := Sym(92)!( 1,48)( 2,47)( 3,69)( 4,68)( 5,67)( 6,66)( 7,65)( 8,64)( 9,63)
(10,62)(11,61)(12,60)(13,59)(14,58)(15,57)(16,56)(17,55)(18,54)(19,53)(20,52)
(21,51)(22,50)(23,49)(24,71)(25,70)(26,92)(27,91)(28,90)(29,89)(30,88)(31,87)
(32,86)(33,85)(34,84)(35,83)(36,82)(37,81)(38,80)(39,79)(40,78)(41,77)(42,76)
(43,75)(44,74)(45,73)(46,72);
poly := sub<Sym(92)|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 >; 
 
References : None.
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