Polytope of Type {88}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {88}*176
Also Known As : 88-gon, {88}. if this polytope has another name.
Group : SmallGroup(176,6)
Rank : 2
Schlafli Type : {88}
Number of vertices, edges, etc : 88, 88
Order of s0s1 : 88
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{88,2} of size 352
{88,4} of size 704
{88,4} of size 704
{88,6} of size 1056
{88,4} of size 1408
{88,8} of size 1408
{88,8} of size 1408
{88,8} of size 1408
{88,8} of size 1408
{88,4} of size 1408
{88,10} of size 1760
Vertex Figure Of :
{2,88} of size 352
{4,88} of size 704
{4,88} of size 704
{6,88} of size 1056
{4,88} of size 1408
{8,88} of size 1408
{8,88} of size 1408
{8,88} of size 1408
{8,88} of size 1408
{4,88} of size 1408
{10,88} of size 1760
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {44}*88
4-fold quotients : {22}*44
8-fold quotients : {11}*22
11-fold quotients : {8}*16
22-fold quotients : {4}*8
44-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {176}*352
3-fold covers : {264}*528
4-fold covers : {352}*704
5-fold covers : {440}*880
6-fold covers : {528}*1056
7-fold covers : {616}*1232
8-fold covers : {704}*1408
9-fold covers : {792}*1584
10-fold covers : {880}*1760
11-fold covers : {968}*1936
Permutation Representation (GAP) :
s0 := ( 2,11)( 3,10)( 4, 9)( 5, 8)( 6, 7)(13,22)(14,21)(15,20)(16,19)(17,18)
(23,34)(24,44)(25,43)(26,42)(27,41)(28,40)(29,39)(30,38)(31,37)(32,36)(33,35)
(45,67)(46,77)(47,76)(48,75)(49,74)(50,73)(51,72)(52,71)(53,70)(54,69)(55,68)
(56,78)(57,88)(58,87)(59,86)(60,85)(61,84)(62,83)(63,82)(64,81)(65,80)
(66,79);;
s1 := ( 1,46)( 2,45)( 3,55)( 4,54)( 5,53)( 6,52)( 7,51)( 8,50)( 9,49)(10,48)
(11,47)(12,57)(13,56)(14,66)(15,65)(16,64)(17,63)(18,62)(19,61)(20,60)(21,59)
(22,58)(23,79)(24,78)(25,88)(26,87)(27,86)(28,85)(29,84)(30,83)(31,82)(32,81)
(33,80)(34,68)(35,67)(36,77)(37,76)(38,75)(39,74)(40,73)(41,72)(42,71)(43,70)
(44,69);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(88)!( 2,11)( 3,10)( 4, 9)( 5, 8)( 6, 7)(13,22)(14,21)(15,20)(16,19)
(17,18)(23,34)(24,44)(25,43)(26,42)(27,41)(28,40)(29,39)(30,38)(31,37)(32,36)
(33,35)(45,67)(46,77)(47,76)(48,75)(49,74)(50,73)(51,72)(52,71)(53,70)(54,69)
(55,68)(56,78)(57,88)(58,87)(59,86)(60,85)(61,84)(62,83)(63,82)(64,81)(65,80)
(66,79);
s1 := Sym(88)!( 1,46)( 2,45)( 3,55)( 4,54)( 5,53)( 6,52)( 7,51)( 8,50)( 9,49)
(10,48)(11,47)(12,57)(13,56)(14,66)(15,65)(16,64)(17,63)(18,62)(19,61)(20,60)
(21,59)(22,58)(23,79)(24,78)(25,88)(26,87)(27,86)(28,85)(29,84)(30,83)(31,82)
(32,81)(33,80)(34,68)(35,67)(36,77)(37,76)(38,75)(39,74)(40,73)(41,72)(42,71)
(43,70)(44,69);
poly := sub<Sym(88)|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 >;
References : None.
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