Polytope of Type {2,2,26}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,26}*208
if this polytope has a name.
Group : SmallGroup(208,50)
Rank : 4
Schlafli Type : {2,2,26}
Number of vertices, edges, etc : 2, 2, 26, 26
Order of s₀s₁s₂s₃ : 26
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,26,2} of size 416
   {2,2,26,4} of size 832
   {2,2,26,6} of size 1248
   {2,2,26,8} of size 1664
Vertex Figure Of :
   {2,2,2,26} of size 416
   {3,2,2,26} of size 624
   {4,2,2,26} of size 832
   {5,2,2,26} of size 1040
   {6,2,2,26} of size 1248
   {7,2,2,26} of size 1456
   {8,2,2,26} of size 1664
   {9,2,2,26} of size 1872
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,13}*104
   13-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,2,52}*416, {2,4,26}*416, {4,2,26}*416
   3-fold covers : {2,6,26}*624, {6,2,26}*624, {2,2,78}*624
   4-fold covers : {2,4,52}*832, {4,2,52}*832, {4,4,26}*832, {2,2,104}*832, {2,8,26}*832, {8,2,26}*832
   5-fold covers : {2,10,26}*1040, {10,2,26}*1040, {2,2,130}*1040
   6-fold covers : {2,12,26}*1248, {12,2,26}*1248, {2,6,52}*1248a, {6,2,52}*1248, {4,6,26}*1248a, {6,4,26}*1248, {2,2,156}*1248, {2,4,78}*1248a, {4,2,78}*1248
   7-fold covers : {2,14,26}*1456, {14,2,26}*1456, {2,2,182}*1456
   8-fold covers : {4,4,52}*1664, {4,8,26}*1664a, {8,4,26}*1664a, {2,8,52}*1664a, {2,4,104}*1664a, {4,8,26}*1664b, {8,4,26}*1664b, {2,8,52}*1664b, {2,4,104}*1664b, {4,4,26}*1664, {2,4,52}*1664, {8,2,52}*1664, {4,2,104}*1664, {2,16,26}*1664, {16,2,26}*1664, {2,2,208}*1664
   9-fold covers : {2,18,26}*1872, {18,2,26}*1872, {2,2,234}*1872, {6,6,26}*1872a, {6,6,26}*1872b, {6,6,26}*1872c, {2,6,78}*1872a, {2,6,78}*1872b, {2,6,78}*1872c, {6,2,78}*1872
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)
(27,28)(29,30);;
s3 := ( 5, 9)( 6, 7)( 8,13)(10,11)(12,17)(14,15)(16,21)(18,19)(20,25)(22,23)
(24,29)(26,27)(28,30);;
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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*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*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(30)!(1,2);
s1 := Sym(30)!(3,4);
s2 := Sym(30)!( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)
(25,26)(27,28)(29,30);
s3 := Sym(30)!( 5, 9)( 6, 7)( 8,13)(10,11)(12,17)(14,15)(16,21)(18,19)(20,25)
(22,23)(24,29)(26,27)(28,30);
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, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*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*s2*s3 >;

to this polytope