Polytope of Type {26}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {26}*52
Also Known As : 26-gon, {26}. if this polytope has another name.
Group : SmallGroup(52,4)
Rank : 2
Schlafli Type : {26}
Number of vertices, edges, etc : 26, 26
Order of s0s1 : 26
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{26,2} of size 104
{26,4} of size 208
{26,6} of size 312
{26,8} of size 416
{26,10} of size 520
{26,12} of size 624
{26,13} of size 676
{26,14} of size 728
{26,16} of size 832
{26,18} of size 936
{26,20} of size 1040
{26,22} of size 1144
{26,24} of size 1248
{26,4} of size 1352
{26,26} of size 1352
{26,26} of size 1352
{26,26} of size 1352
{26,28} of size 1456
{26,30} of size 1560
{26,32} of size 1664
{26,34} of size 1768
{26,36} of size 1872
{26,38} of size 1976
Vertex Figure Of :
{2,26} of size 104
{4,26} of size 208
{6,26} of size 312
{8,26} of size 416
{10,26} of size 520
{12,26} of size 624
{13,26} of size 676
{14,26} of size 728
{16,26} of size 832
{18,26} of size 936
{20,26} of size 1040
{22,26} of size 1144
{24,26} of size 1248
{4,26} of size 1352
{26,26} of size 1352
{26,26} of size 1352
{26,26} of size 1352
{28,26} of size 1456
{30,26} of size 1560
{32,26} of size 1664
{34,26} of size 1768
{36,26} of size 1872
{38,26} of size 1976
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {13}*26
13-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {52}*104
3-fold covers : {78}*156
4-fold covers : {104}*208
5-fold covers : {130}*260
6-fold covers : {156}*312
7-fold covers : {182}*364
8-fold covers : {208}*416
9-fold covers : {234}*468
10-fold covers : {260}*520
11-fold covers : {286}*572
12-fold covers : {312}*624
13-fold covers : {338}*676
14-fold covers : {364}*728
15-fold covers : {390}*780
16-fold covers : {416}*832
17-fold covers : {442}*884
18-fold covers : {468}*936
19-fold covers : {494}*988
20-fold covers : {520}*1040
21-fold covers : {546}*1092
22-fold covers : {572}*1144
23-fold covers : {598}*1196
24-fold covers : {624}*1248
25-fold covers : {650}*1300
26-fold covers : {676}*1352
27-fold covers : {702}*1404
28-fold covers : {728}*1456
29-fold covers : {754}*1508
30-fold covers : {780}*1560
31-fold covers : {806}*1612
32-fold covers : {832}*1664
33-fold covers : {858}*1716
34-fold covers : {884}*1768
35-fold covers : {910}*1820
36-fold covers : {936}*1872
37-fold covers : {962}*1924
38-fold covers : {988}*1976
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)
(23,24)(25,26);;
s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,17)(14,15)(16,21)(18,19)
(20,25)(22,23)(24,26);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(26)!( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)
(21,22)(23,24)(25,26);
s1 := Sym(26)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,17)(14,15)(16,21)
(18,19)(20,25)(22,23)(24,26);
poly := sub<Sym(26)|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 >;
References : None.
to this polytope