Polytope of Type {26,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {26,2}*104
if this polytope has a name.
Group : SmallGroup(104,13)
Rank : 3
Schlafli Type : {26,2}
Number of vertices, edges, etc : 26, 26, 2
Order of s0s1s2 : 26
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 :
{26,2,2} of size 208
{26,2,3} of size 312
{26,2,4} of size 416
{26,2,5} of size 520
{26,2,6} of size 624
{26,2,7} of size 728
{26,2,8} of size 832
{26,2,9} of size 936
{26,2,10} of size 1040
{26,2,11} of size 1144
{26,2,12} of size 1248
{26,2,13} of size 1352
{26,2,14} of size 1456
{26,2,15} of size 1560
{26,2,16} of size 1664
{26,2,17} of size 1768
{26,2,18} of size 1872
{26,2,19} of size 1976
Vertex Figure Of :
{2,26,2} of size 208
{4,26,2} of size 416
{6,26,2} of size 624
{8,26,2} of size 832
{10,26,2} of size 1040
{12,26,2} of size 1248
{13,26,2} of size 1352
{14,26,2} of size 1456
{16,26,2} of size 1664
{18,26,2} of size 1872
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {13,2}*52
13-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {52,2}*208, {26,4}*208
3-fold covers : {26,6}*312, {78,2}*312
4-fold covers : {52,4}*416, {104,2}*416, {26,8}*416
5-fold covers : {26,10}*520, {130,2}*520
6-fold covers : {26,12}*624, {52,6}*624a, {156,2}*624, {78,4}*624a
7-fold covers : {26,14}*728, {182,2}*728
8-fold covers : {104,4}*832a, {52,4}*832, {104,4}*832b, {52,8}*832a, {52,8}*832b, {208,2}*832, {26,16}*832
9-fold covers : {26,18}*936, {234,2}*936, {78,6}*936a, {78,6}*936b, {78,6}*936c
10-fold covers : {26,20}*1040, {52,10}*1040, {260,2}*1040, {130,4}*1040
11-fold covers : {26,22}*1144, {286,2}*1144
12-fold covers : {26,24}*1248, {104,6}*1248, {52,12}*1248, {156,4}*1248a, {312,2}*1248, {78,8}*1248, {52,6}*1248, {78,6}*1248, {78,4}*1248
13-fold covers : {338,2}*1352, {26,26}*1352a, {26,26}*1352c
14-fold covers : {26,28}*1456, {52,14}*1456, {364,2}*1456, {182,4}*1456
15-fold covers : {26,30}*1560, {78,10}*1560, {130,6}*1560, {390,2}*1560
16-fold covers : {52,8}*1664a, {104,4}*1664a, {104,8}*1664a, {104,8}*1664b, {104,8}*1664c, {104,8}*1664d, {52,16}*1664a, {208,4}*1664a, {52,16}*1664b, {208,4}*1664b, {52,4}*1664, {104,4}*1664b, {52,8}*1664b, {26,32}*1664, {416,2}*1664
17-fold covers : {26,34}*1768, {442,2}*1768
18-fold covers : {26,36}*1872, {52,18}*1872a, {468,2}*1872, {234,4}*1872a, {156,6}*1872a, {78,12}*1872a, {78,12}*1872b, {156,6}*1872b, {156,6}*1872c, {78,12}*1872c, {52,4}*1872, {78,4}*1872, {52,6}*1872
19-fold covers : {26,38}*1976, {494,2}*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);;
s2 := (27,28);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(28)!( 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(28)!( 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);
s2 := Sym(28)!(27,28);
poly := sub<Sym(28)|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 >;
to this polytope