Polytope of Type {13,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {13,2}*52
if this polytope has a name.
Group : SmallGroup(52,4)
Rank : 3
Schlafli Type : {13,2}
Number of vertices, edges, etc : 13, 13, 2
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 :
   {13,2,2} of size 104
   {13,2,3} of size 156
   {13,2,4} of size 208
   {13,2,5} of size 260
   {13,2,6} of size 312
   {13,2,7} of size 364
   {13,2,8} of size 416
   {13,2,9} of size 468
   {13,2,10} of size 520
   {13,2,11} of size 572
   {13,2,12} of size 624
   {13,2,13} of size 676
   {13,2,14} of size 728
   {13,2,15} of size 780
   {13,2,16} of size 832
   {13,2,17} of size 884
   {13,2,18} of size 936
   {13,2,19} of size 988
   {13,2,20} of size 1040
   {13,2,21} of size 1092
   {13,2,22} of size 1144
   {13,2,23} of size 1196
   {13,2,24} of size 1248
   {13,2,25} of size 1300
   {13,2,26} of size 1352
   {13,2,27} of size 1404
   {13,2,28} of size 1456
   {13,2,29} of size 1508
   {13,2,30} of size 1560
   {13,2,31} of size 1612
   {13,2,32} of size 1664
   {13,2,33} of size 1716
   {13,2,34} of size 1768
   {13,2,35} of size 1820
   {13,2,36} of size 1872
   {13,2,37} of size 1924
   {13,2,38} of size 1976
Vertex Figure Of :
   {2,13,2} of size 104
   {26,13,2} of size 1352
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {26,2}*104
   3-fold covers : {39,2}*156
   4-fold covers : {52,2}*208, {26,4}*208
   5-fold covers : {65,2}*260
   6-fold covers : {26,6}*312, {78,2}*312
   7-fold covers : {91,2}*364
   8-fold covers : {52,4}*416, {104,2}*416, {26,8}*416
   9-fold covers : {117,2}*468, {39,6}*468
   10-fold covers : {26,10}*520, {130,2}*520
   11-fold covers : {143,2}*572
   12-fold covers : {26,12}*624, {52,6}*624a, {156,2}*624, {78,4}*624a, {39,6}*624, {39,4}*624
   13-fold covers : {169,2}*676, {13,26}*676
   14-fold covers : {26,14}*728, {182,2}*728
   15-fold covers : {195,2}*780
   16-fold covers : {104,4}*832a, {52,4}*832, {104,4}*832b, {52,8}*832a, {52,8}*832b, {208,2}*832, {26,16}*832
   17-fold covers : {221,2}*884
   18-fold covers : {26,18}*936, {234,2}*936, {78,6}*936a, {78,6}*936b, {78,6}*936c
   19-fold covers : {247,2}*988
   20-fold covers : {26,20}*1040, {52,10}*1040, {260,2}*1040, {130,4}*1040
   21-fold covers : {273,2}*1092
   22-fold covers : {26,22}*1144, {286,2}*1144
   23-fold covers : {299,2}*1196
   24-fold covers : {26,24}*1248, {104,6}*1248, {52,12}*1248, {156,4}*1248a, {312,2}*1248, {78,8}*1248, {39,12}*1248, {39,8}*1248, {52,6}*1248, {78,6}*1248, {78,4}*1248
   25-fold covers : {325,2}*1300, {65,10}*1300
   26-fold covers : {338,2}*1352, {26,26}*1352a, {26,26}*1352c
   27-fold covers : {351,2}*1404, {117,6}*1404, {39,6}*1404
   28-fold covers : {26,28}*1456, {52,14}*1456, {364,2}*1456, {182,4}*1456
   29-fold covers : {377,2}*1508
   30-fold covers : {26,30}*1560, {78,10}*1560, {130,6}*1560, {390,2}*1560
   31-fold covers : {403,2}*1612
   32-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
   33-fold covers : {429,2}*1716
   34-fold covers : {26,34}*1768, {442,2}*1768
   35-fold covers : {455,2}*1820
   36-fold covers : {26,36}*1872, {52,18}*1872a, {468,2}*1872, {234,4}*1872a, {117,4}*1872, {156,6}*1872a, {78,12}*1872a, {78,12}*1872b, {156,6}*1872b, {156,6}*1872c, {78,12}*1872c, {52,4}*1872, {78,4}*1872, {39,12}*1872, {39,6}*1872, {52,6}*1872
   37-fold covers : {481,2}*1924
   38-fold covers : {26,38}*1976, {494,2}*1976
Permutation Representation (GAP) :

s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12);;
s2 := (14,15);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(15)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13);
s1 := Sym(15)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12);
s2 := Sym(15)!(14,15);
poly := sub<Sym(15)|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 >;

to this polytope