Polytope of Type {4,2,26}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,26}*416
if this polytope has a name.
Group : SmallGroup(416,216)
Rank : 4
Schlafli Type : {4,2,26}
Number of vertices, edges, etc : 4, 4, 26, 26
Order of s₀s₁s₂s₃ : 52
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,2,26,2} of size 832
   {4,2,26,4} of size 1664
Vertex Figure Of :
   {2,4,2,26} of size 832
   {3,4,2,26} of size 1248
   {4,4,2,26} of size 1664
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,2,13}*208, {2,2,26}*208
   4-fold quotients : {2,2,13}*104
   13-fold quotients : {4,2,2}*32
   26-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,52}*832, {4,4,26}*832, {8,2,26}*832
   3-fold covers : {12,2,26}*1248, {4,6,26}*1248a, {4,2,78}*1248
   4-fold covers : {4,4,52}*1664, {4,8,26}*1664a, {8,4,26}*1664a, {4,8,26}*1664b, {8,4,26}*1664b, {4,4,26}*1664, {8,2,52}*1664, {4,2,104}*1664, {16,2,26}*1664
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2)(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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*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(30)!(2,3);
s1 := Sym(30)!(1,2)(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*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s1*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 >;

to this polytope