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Polytope of Type {13,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {13,2,2}*104
if this polytope has a name.
Group : SmallGroup(104,13)
Rank : 4
Schlafli Type : {13,2,2}
Number of vertices, edges, etc : 13, 13, 2, 2
Order of s0s1s2s3 : 26
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {13,2,2,2} of size 208
   {13,2,2,3} of size 312
   {13,2,2,4} of size 416
   {13,2,2,5} of size 520
   {13,2,2,6} of size 624
   {13,2,2,7} of size 728
   {13,2,2,8} of size 832
   {13,2,2,9} of size 936
   {13,2,2,10} of size 1040
   {13,2,2,11} of size 1144
   {13,2,2,12} of size 1248
   {13,2,2,13} of size 1352
   {13,2,2,14} of size 1456
   {13,2,2,15} of size 1560
   {13,2,2,16} of size 1664
   {13,2,2,17} of size 1768
   {13,2,2,18} of size 1872
   {13,2,2,19} of size 1976
Vertex Figure Of :
   {2,13,2,2} of size 208
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {13,2,4}*208, {26,2,2}*208
   3-fold covers : {13,2,6}*312, {39,2,2}*312
   4-fold covers : {13,2,8}*416, {52,2,2}*416, {26,2,4}*416, {26,4,2}*416
   5-fold covers : {13,2,10}*520, {65,2,2}*520
   6-fold covers : {13,2,12}*624, {39,2,4}*624, {26,2,6}*624, {26,6,2}*624, {78,2,2}*624
   7-fold covers : {13,2,14}*728, {91,2,2}*728
   8-fold covers : {13,2,16}*832, {52,4,2}*832, {52,2,4}*832, {26,4,4}*832, {104,2,2}*832, {26,2,8}*832, {26,8,2}*832
   9-fold covers : {13,2,18}*936, {117,2,2}*936, {39,2,6}*936, {39,6,2}*936
   10-fold covers : {13,2,20}*1040, {65,2,4}*1040, {26,2,10}*1040, {26,10,2}*1040, {130,2,2}*1040
   11-fold covers : {13,2,22}*1144, {143,2,2}*1144
   12-fold covers : {13,2,24}*1248, {39,2,8}*1248, {26,2,12}*1248, {26,12,2}*1248, {52,2,6}*1248, {52,6,2}*1248a, {26,4,6}*1248, {26,6,4}*1248a, {156,2,2}*1248, {78,2,4}*1248, {78,4,2}*1248a, {39,6,2}*1248, {39,4,2}*1248
   13-fold covers : {169,2,2}*1352, {13,2,26}*1352, {13,26,2}*1352
   14-fold covers : {13,2,28}*1456, {91,2,4}*1456, {26,2,14}*1456, {26,14,2}*1456, {182,2,2}*1456
   15-fold covers : {13,2,30}*1560, {39,2,10}*1560, {65,2,6}*1560, {195,2,2}*1560
   16-fold covers : {13,2,32}*1664, {52,4,4}*1664, {26,4,8}*1664a, {26,8,4}*1664a, {52,8,2}*1664a, {104,4,2}*1664a, {26,4,8}*1664b, {26,8,4}*1664b, {52,8,2}*1664b, {104,4,2}*1664b, {26,4,4}*1664, {52,4,2}*1664, {52,2,8}*1664, {104,2,4}*1664, {26,2,16}*1664, {26,16,2}*1664, {208,2,2}*1664
   17-fold covers : {13,2,34}*1768, {221,2,2}*1768
   18-fold covers : {13,2,36}*1872, {117,2,4}*1872, {26,2,18}*1872, {26,18,2}*1872, {234,2,2}*1872, {39,2,12}*1872, {39,6,4}*1872, {26,6,6}*1872a, {26,6,6}*1872b, {26,6,6}*1872c, {78,6,2}*1872a, {78,2,6}*1872, {78,6,2}*1872b, {78,6,2}*1872c
   19-fold covers : {13,2,38}*1976, {247,2,2}*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);;
s3 := (16,17);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, 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(17)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13);
s1 := Sym(17)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12);
s2 := Sym(17)!(14,15);
s3 := Sym(17)!(16,17);
poly := sub<Sym(17)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, 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 >; 
 

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