Part of the Atlas of Small Regular Polytopes

Polytope of Type {98,2}

Atlas Canonical Name {98,2}*392

Overview

Group
SmallGroup(392,12)
Rank
3
Schläfli Type
{98,2}
Vertices, edges, …
98, 98, 2
Order of s0s1s2
98
Order of s0s1s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable
  • Flat
  • Self-Petrie

Quotients maximal quotients in bold

2-fold

7-fold

14-fold

49-fold

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

Representations

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 >;