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Polytope of Type {26,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {26,2,2}*208
if this polytope has a name.
Group : SmallGroup(208,50)
Rank : 4
Schlafli Type : {26,2,2}
Number of vertices, edges, etc : 26, 26, 2, 2
Order of s0s1s2s3 : 26
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {26,2,2,2} of size 416
   {26,2,2,3} of size 624
   {26,2,2,4} of size 832
   {26,2,2,5} of size 1040
   {26,2,2,6} of size 1248
   {26,2,2,7} of size 1456
   {26,2,2,8} of size 1664
   {26,2,2,9} of size 1872
Vertex Figure Of :
   {2,26,2,2} of size 416
   {4,26,2,2} of size 832
   {6,26,2,2} of size 1248
   {8,26,2,2} of size 1664
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {13,2,2}*104
   13-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {52,2,2}*416, {26,2,4}*416, {26,4,2}*416
   3-fold covers : {26,2,6}*624, {26,6,2}*624, {78,2,2}*624
   4-fold covers : {52,4,2}*832, {52,2,4}*832, {26,4,4}*832, {104,2,2}*832, {26,2,8}*832, {26,8,2}*832
   5-fold covers : {26,2,10}*1040, {26,10,2}*1040, {130,2,2}*1040
   6-fold covers : {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
   7-fold covers : {26,2,14}*1456, {26,14,2}*1456, {182,2,2}*1456
   8-fold covers : {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
   9-fold covers : {26,2,18}*1872, {26,18,2}*1872, {234,2,2}*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
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 := (27,28);;
s3 := (29,30);;
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*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(30)!( 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(30)!( 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(30)!(27,28);
s3 := Sym(30)!(29,30);
poly := sub<Sym(30)|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*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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