Polytope of Type {2,86}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,86}*344
if this polytope has a name.
Group : SmallGroup(344,11)
Rank : 3
Schlafli Type : {2,86}
Number of vertices, edges, etc : 2, 86, 86
Order of s₀s₁s₂ : 86
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,86,2} of size 688
   {2,86,4} of size 1376
Vertex Figure Of :
   {2,2,86} of size 688
   {3,2,86} of size 1032
   {4,2,86} of size 1376
   {5,2,86} of size 1720
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,43}*172
   43-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,172}*688, {4,86}*688
   3-fold covers : {6,86}*1032, {2,258}*1032
   4-fold covers : {4,172}*1376, {8,86}*1376, {2,344}*1376
   5-fold covers : {10,86}*1720, {2,430}*1720
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope