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Polytope of Type {94}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {94}*188
Also Known As : 94-gon, {94}. if this polytope has another name.
Group : SmallGroup(188,3)
Rank : 2
Schlafli Type : {94}
Number of vertices, edges, etc : 94, 94
Order of s₀s₁ : 94
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {94,2} of size 376
   {94,4} of size 752
   {94,6} of size 1128
   {94,8} of size 1504
   {94,10} of size 1880
Vertex Figure Of :
   {2,94} of size 376
   {4,94} of size 752
   {6,94} of size 1128
   {8,94} of size 1504
   {10,94} of size 1880
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {47}*94
   47-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   2-fold covers : {188}*376
   3-fold covers : {282}*564
   4-fold covers : {376}*752
   5-fold covers : {470}*940
   6-fold covers : {564}*1128
   7-fold covers : {658}*1316
   8-fold covers : {752}*1504
   9-fold covers : {846}*1692
   10-fold covers : {940}*1880
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope