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Polytope of Type {2,26,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,26,2}*208
if this polytope has a name.
Group : SmallGroup(208,50)
Rank : 4
Schlafli Type : {2,26,2}
Number of vertices, edges, etc : 2, 26, 26, 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 :
   {2,26,2,2} of size 416
   {2,26,2,3} of size 624
   {2,26,2,4} of size 832
   {2,26,2,5} of size 1040
   {2,26,2,6} of size 1248
   {2,26,2,7} of size 1456
   {2,26,2,8} of size 1664
   {2,26,2,9} of size 1872
Vertex Figure Of :
   {2,2,26,2} of size 416
   {3,2,26,2} of size 624
   {4,2,26,2} of size 832
   {5,2,26,2} of size 1040
   {6,2,26,2} of size 1248
   {7,2,26,2} of size 1456
   {8,2,26,2} of size 1664
   {9,2,26,2} of size 1872
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,13,2}*104
   13-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,52,2}*416, {2,26,4}*416, {4,26,2}*416
   3-fold covers : {2,26,6}*624, {6,26,2}*624, {2,78,2}*624
   4-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
   5-fold covers : {2,26,10}*1040, {10,26,2}*1040, {2,130,2}*1040
   6-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
   7-fold covers : {2,26,14}*1456, {14,26,2}*1456, {2,182,2}*1456
   8-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
   9-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
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)
(25,26)(27,28);;
s2 := ( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,15)(12,13)(14,19)(16,17)(18,23)(20,21)
(22,27)(24,25)(26,28);;
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*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*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(30)!(1,2);
s1 := Sym(30)!( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)
(23,24)(25,26)(27,28);
s2 := Sym(30)!( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,15)(12,13)(14,19)(16,17)(18,23)
(20,21)(22,27)(24,25)(26,28);
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*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*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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