Polytope of Type {2,26}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,26}*104
if this polytope has a name.
Group : SmallGroup(104,13)
Rank : 3
Schlafli Type : {2,26}
Number of vertices, edges, etc : 2, 26, 26
Order of s0s1s2 : 26
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,26,2} of size 208
{2,26,4} of size 416
{2,26,6} of size 624
{2,26,8} of size 832
{2,26,10} of size 1040
{2,26,12} of size 1248
{2,26,13} of size 1352
{2,26,14} of size 1456
{2,26,16} of size 1664
{2,26,18} of size 1872
Vertex Figure Of :
{2,2,26} of size 208
{3,2,26} of size 312
{4,2,26} of size 416
{5,2,26} of size 520
{6,2,26} of size 624
{7,2,26} of size 728
{8,2,26} of size 832
{9,2,26} of size 936
{10,2,26} of size 1040
{11,2,26} of size 1144
{12,2,26} of size 1248
{13,2,26} of size 1352
{14,2,26} of size 1456
{15,2,26} of size 1560
{16,2,26} of size 1664
{17,2,26} of size 1768
{18,2,26} of size 1872
{19,2,26} of size 1976
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,13}*52
13-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,52}*208, {4,26}*208
3-fold covers : {6,26}*312, {2,78}*312
4-fold covers : {4,52}*416, {2,104}*416, {8,26}*416
5-fold covers : {10,26}*520, {2,130}*520
6-fold covers : {12,26}*624, {6,52}*624a, {2,156}*624, {4,78}*624a
7-fold covers : {14,26}*728, {2,182}*728
8-fold covers : {4,104}*832a, {4,52}*832, {4,104}*832b, {8,52}*832a, {8,52}*832b, {2,208}*832, {16,26}*832
9-fold covers : {18,26}*936, {2,234}*936, {6,78}*936a, {6,78}*936b, {6,78}*936c
10-fold covers : {20,26}*1040, {10,52}*1040, {2,260}*1040, {4,130}*1040
11-fold covers : {22,26}*1144, {2,286}*1144
12-fold covers : {24,26}*1248, {6,104}*1248, {12,52}*1248, {4,156}*1248a, {2,312}*1248, {8,78}*1248, {6,52}*1248, {6,78}*1248, {4,78}*1248
13-fold covers : {2,338}*1352, {26,26}*1352a, {26,26}*1352b
14-fold covers : {28,26}*1456, {14,52}*1456, {2,364}*1456, {4,182}*1456
15-fold covers : {30,26}*1560, {10,78}*1560, {6,130}*1560, {2,390}*1560
16-fold covers : {8,52}*1664a, {4,104}*1664a, {8,104}*1664a, {8,104}*1664b, {8,104}*1664c, {8,104}*1664d, {16,52}*1664a, {4,208}*1664a, {16,52}*1664b, {4,208}*1664b, {4,52}*1664, {4,104}*1664b, {8,52}*1664b, {32,26}*1664, {2,416}*1664
17-fold covers : {34,26}*1768, {2,442}*1768
18-fold covers : {36,26}*1872, {18,52}*1872a, {2,468}*1872, {4,234}*1872a, {6,156}*1872a, {12,78}*1872a, {12,78}*1872b, {6,156}*1872b, {6,156}*1872c, {12,78}*1872c, {4,52}*1872, {4,78}*1872, {6,52}*1872
19-fold covers : {38,26}*1976, {2,494}*1976
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)
(25,26)(27,28);;
s2 := ( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,15)(12,13)(14,19)(16,17)(18,23)(20,21)
(22,27)(24,25)(26,28);;
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*s1*s0*s1, s0*s2*s0*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(28)!(1,2);
s1 := Sym(28)!( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)
(23,24)(25,26)(27,28);
s2 := Sym(28)!( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,15)(12,13)(14,19)(16,17)(18,23)
(20,21)(22,27)(24,25)(26,28);
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*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope