Polytope of Type {98,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {98,2}*392
if this polytope has a name.
Group : SmallGroup(392,12)
Rank : 3
Schlafli Type : {98,2}
Number of vertices, edges, etc : 98, 98, 2
Order of s₀s₁s₂ : 98
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {98,2,2} of size 784
   {98,2,3} of size 1176
   {98,2,4} of size 1568
   {98,2,5} of size 1960
Vertex Figure Of :
   {2,98,2} of size 784
   {4,98,2} of size 1568
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {49,2}*196
   7-fold quotients : {14,2}*56
   14-fold quotients : {7,2}*28
   49-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {196,2}*784, {98,4}*784
   3-fold covers : {98,6}*1176, {294,2}*1176
   4-fold covers : {196,4}*1568, {392,2}*1568, {98,8}*1568
   5-fold covers : {98,10}*1960, {490,2}*1960
Permutation Representation (GAP) :

s0 := ( 2, 7)( 3, 6)( 4, 5)( 8,44)( 9,43)(10,49)(11,48)(12,47)(13,46)(14,45)
(15,37)(16,36)(17,42)(18,41)(19,40)(20,39)(21,38)(22,30)(23,29)(24,35)(25,34)
(26,33)(27,32)(28,31)(51,56)(52,55)(53,54)(57,93)(58,92)(59,98)(60,97)(61,96)
(62,95)(63,94)(64,86)(65,85)(66,91)(67,90)(68,89)(69,88)(70,87)(71,79)(72,78)
(73,84)(74,83)(75,82)(76,81)(77,80);;
s1 := ( 1,57)( 2,63)( 3,62)( 4,61)( 5,60)( 6,59)( 7,58)( 8,50)( 9,56)(10,55)
(11,54)(12,53)(13,52)(14,51)(15,93)(16,92)(17,98)(18,97)(19,96)(20,95)(21,94)
(22,86)(23,85)(24,91)(25,90)(26,89)(27,88)(28,87)(29,79)(30,78)(31,84)(32,83)
(33,82)(34,81)(35,80)(36,72)(37,71)(38,77)(39,76)(40,75)(41,74)(42,73)(43,65)
(44,64)(45,70)(46,69)(47,68)(48,67)(49,66);;
s2 := ( 99,100);;
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*s2*s0*s2, s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(100)!( 2, 7)( 3, 6)( 4, 5)( 8,44)( 9,43)(10,49)(11,48)(12,47)(13,46)
(14,45)(15,37)(16,36)(17,42)(18,41)(19,40)(20,39)(21,38)(22,30)(23,29)(24,35)
(25,34)(26,33)(27,32)(28,31)(51,56)(52,55)(53,54)(57,93)(58,92)(59,98)(60,97)
(61,96)(62,95)(63,94)(64,86)(65,85)(66,91)(67,90)(68,89)(69,88)(70,87)(71,79)
(72,78)(73,84)(74,83)(75,82)(76,81)(77,80);
s1 := Sym(100)!( 1,57)( 2,63)( 3,62)( 4,61)( 5,60)( 6,59)( 7,58)( 8,50)( 9,56)
(10,55)(11,54)(12,53)(13,52)(14,51)(15,93)(16,92)(17,98)(18,97)(19,96)(20,95)
(21,94)(22,86)(23,85)(24,91)(25,90)(26,89)(27,88)(28,87)(29,79)(30,78)(31,84)
(32,83)(33,82)(34,81)(35,80)(36,72)(37,71)(38,77)(39,76)(40,75)(41,74)(42,73)
(43,65)(44,64)(45,70)(46,69)(47,68)(48,67)(49,66);
s2 := Sym(100)!( 99,100);
poly := sub<Sym(100)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

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

to this polytope