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Polytope of Type {2,13,2}

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

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