Polytope of Type {98}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {98}*196
Also Known As : 98-gon, {98}. if this polytope has another name.
Group : SmallGroup(196,3)
Rank : 2
Schlafli Type : {98}
Number of vertices, edges, etc : 98, 98
Order of s0s1 : 98
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{98,2} of size 392
{98,4} of size 784
{98,6} of size 1176
{98,8} of size 1568
{98,10} of size 1960
Vertex Figure Of :
{2,98} of size 392
{4,98} of size 784
{6,98} of size 1176
{8,98} of size 1568
{10,98} of size 1960
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {49}*98
7-fold quotients : {14}*28
14-fold quotients : {7}*14
49-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {196}*392
3-fold covers : {294}*588
4-fold covers : {392}*784
5-fold covers : {490}*980
6-fold covers : {588}*1176
7-fold covers : {686}*1372
8-fold covers : {784}*1568
9-fold covers : {882}*1764
10-fold covers : {980}*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);;
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*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(98)!( 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(98)!( 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);
poly := sub<Sym(98)|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*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
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