Polytope of Type {2,26,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,26,2,2}*416
if this polytope has a name.
Group : SmallGroup(416,234)
Rank : 5
Schlafli Type : {2,26,2,2}
Number of vertices, edges, etc : 2, 26, 26, 2, 2
Order of s₀s₁s₂s₃s₄ : 26
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,26,2,2,2} of size 832
   {2,26,2,2,3} of size 1248
   {2,26,2,2,4} of size 1664
Vertex Figure Of :
   {2,2,26,2,2} of size 832
   {3,2,26,2,2} of size 1248
   {4,2,26,2,2} of size 1664
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,13,2,2}*208
   13-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,52,2,2}*832, {2,26,2,4}*832, {2,26,4,2}*832, {4,26,2,2}*832
   3-fold covers : {2,26,2,6}*1248, {2,26,6,2}*1248, {6,26,2,2}*1248, {2,78,2,2}*1248
   4-fold covers : {2,26,4,4}*1664, {2,52,4,2}*1664, {4,52,2,2}*1664, {4,26,2,4}*1664, {4,26,4,2}*1664, {2,52,2,4}*1664, {2,26,2,8}*1664, {2,26,8,2}*1664, {8,26,2,2}*1664, {2,104,2,2}*1664
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);;
s4 := (31,32);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, 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(32)!(1,2);
s1 := Sym(32)!( 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(32)!( 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(32)!(29,30);
s4 := Sym(32)!(31,32);
poly := sub<Sym(32)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, 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 >;

to this polytope