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Polytope of Type {26,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {26,2,3}*312
if this polytope has a name.
Group : SmallGroup(312,54)
Rank : 4
Schlafli Type : {26,2,3}
Number of vertices, edges, etc : 26, 26, 3, 3
Order of s0s1s2s3 : 78
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {26,2,3,2} of size 624
   {26,2,3,3} of size 1248
   {26,2,3,4} of size 1248
   {26,2,3,6} of size 1872
Vertex Figure Of :
   {2,26,2,3} of size 624
   {4,26,2,3} of size 1248
   {6,26,2,3} of size 1872
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {13,2,3}*156
   13-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {52,2,3}*624, {26,2,6}*624
   3-fold covers : {26,2,9}*936, {26,6,3}*936, {78,2,3}*936
   4-fold covers : {104,2,3}*1248, {26,2,12}*1248, {52,2,6}*1248, {26,4,6}*1248, {26,4,3}*1248
   5-fold covers : {26,2,15}*1560, {130,2,3}*1560
   6-fold covers : {52,2,9}*1872, {26,2,18}*1872, {52,6,3}*1872, {156,2,3}*1872, {26,6,6}*1872a, {26,6,6}*1872b, {78,2,6}*1872
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 := (28,29);;
s3 := (27,28);;
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*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*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(29)!( 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(29)!( 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(29)!(28,29);
s3 := Sym(29)!(27,28);
poly := sub<Sym(29)|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*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*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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