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Polytope of Type {3,2,26}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,26}*312
if this polytope has a name.
Group : SmallGroup(312,54)
Rank : 4
Schlafli Type : {3,2,26}
Number of vertices, edges, etc : 3, 3, 26, 26
Order of s0s1s2s3 : 78
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,26,2} of size 624
   {3,2,26,4} of size 1248
   {3,2,26,6} of size 1872
Vertex Figure Of :
   {2,3,2,26} of size 624
   {3,3,2,26} of size 1248
   {4,3,2,26} of size 1248
   {6,3,2,26} of size 1872
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,13}*156
   13-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,52}*624, {6,2,26}*624
   3-fold covers : {9,2,26}*936, {3,6,26}*936, {3,2,78}*936
   4-fold covers : {3,2,104}*1248, {12,2,26}*1248, {6,2,52}*1248, {6,4,26}*1248, {3,4,26}*1248
   5-fold covers : {15,2,26}*1560, {3,2,130}*1560
   6-fold covers : {9,2,52}*1872, {18,2,26}*1872, {3,6,52}*1872, {3,2,156}*1872, {6,6,26}*1872a, {6,6,26}*1872c, {6,2,78}*1872
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)
(26,27)(28,29);;
s3 := ( 4, 8)( 5, 6)( 7,12)( 9,10)(11,16)(13,14)(15,20)(17,18)(19,24)(21,22)
(23,28)(25,26)(27,29);;
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, 
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(29)!(2,3);
s1 := Sym(29)!(1,2);
s2 := Sym(29)!( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)
(24,25)(26,27)(28,29);
s3 := Sym(29)!( 4, 8)( 5, 6)( 7,12)( 9,10)(11,16)(13,14)(15,20)(17,18)(19,24)
(21,22)(23,28)(25,26)(27,29);
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, s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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