Polytope of Type {2,92}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,92}*368
if this polytope has a name.
Group : SmallGroup(368,29)
Rank : 3
Schlafli Type : {2,92}
Number of vertices, edges, etc : 2, 92, 92
Order of s₀s₁s₂ : 92
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,92,2} of size 736
   {2,92,4} of size 1472
Vertex Figure Of :
   {2,2,92} of size 736
   {3,2,92} of size 1104
   {4,2,92} of size 1472
   {5,2,92} of size 1840
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,46}*184
   4-fold quotients : {2,23}*92
   23-fold quotients : {2,4}*16
   46-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,92}*736, {2,184}*736
   3-fold covers : {6,92}*1104a, {2,276}*1104
   4-fold covers : {8,92}*1472a, {4,184}*1472a, {8,92}*1472b, {4,184}*1472b, {4,92}*1472, {2,368}*1472
   5-fold covers : {10,92}*1840, {2,460}*1840
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4,25)( 5,24)( 6,23)( 7,22)( 8,21)( 9,20)(10,19)(11,18)(12,17)(13,16)
(14,15)(27,48)(28,47)(29,46)(30,45)(31,44)(32,43)(33,42)(34,41)(35,40)(36,39)
(37,38)(49,72)(50,94)(51,93)(52,92)(53,91)(54,90)(55,89)(56,88)(57,87)(58,86)
(59,85)(60,84)(61,83)(62,82)(63,81)(64,80)(65,79)(66,78)(67,77)(68,76)(69,75)
(70,74)(71,73);;
s2 := ( 3,50)( 4,49)( 5,71)( 6,70)( 7,69)( 8,68)( 9,67)(10,66)(11,65)(12,64)
(13,63)(14,62)(15,61)(16,60)(17,59)(18,58)(19,57)(20,56)(21,55)(22,54)(23,53)
(24,52)(25,51)(26,73)(27,72)(28,94)(29,93)(30,92)(31,91)(32,90)(33,89)(34,88)
(35,87)(36,86)(37,85)(38,84)(39,83)(40,82)(41,81)(42,80)(43,79)(44,78)(45,77)
(46,76)(47,75)(48,74);;
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*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(94)!(1,2);
s1 := Sym(94)!( 4,25)( 5,24)( 6,23)( 7,22)( 8,21)( 9,20)(10,19)(11,18)(12,17)
(13,16)(14,15)(27,48)(28,47)(29,46)(30,45)(31,44)(32,43)(33,42)(34,41)(35,40)
(36,39)(37,38)(49,72)(50,94)(51,93)(52,92)(53,91)(54,90)(55,89)(56,88)(57,87)
(58,86)(59,85)(60,84)(61,83)(62,82)(63,81)(64,80)(65,79)(66,78)(67,77)(68,76)
(69,75)(70,74)(71,73);
s2 := Sym(94)!( 3,50)( 4,49)( 5,71)( 6,70)( 7,69)( 8,68)( 9,67)(10,66)(11,65)
(12,64)(13,63)(14,62)(15,61)(16,60)(17,59)(18,58)(19,57)(20,56)(21,55)(22,54)
(23,53)(24,52)(25,51)(26,73)(27,72)(28,94)(29,93)(30,92)(31,91)(32,90)(33,89)
(34,88)(35,87)(36,86)(37,85)(38,84)(39,83)(40,82)(41,81)(42,80)(43,79)(44,78)
(45,77)(46,76)(47,75)(48,74);
poly := sub<Sym(94)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope