Polytope of Type {26,4,2}

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

s0 := ( 2,13)( 3,12)( 4,11)( 5,10)( 6, 9)( 7, 8)(15,26)(16,25)(17,24)(18,23)
(19,22)(20,21)(28,39)(29,38)(30,37)(31,36)(32,35)(33,34)(41,52)(42,51)(43,50)
(44,49)(45,48)(46,47);;
s1 := ( 1, 2)( 3,13)( 4,12)( 5,11)( 6,10)( 7, 9)(14,15)(16,26)(17,25)(18,24)
(19,23)(20,22)(27,41)(28,40)(29,52)(30,51)(31,50)(32,49)(33,48)(34,47)(35,46)
(36,45)(37,44)(38,43)(39,42);;
s2 := ( 1,27)( 2,28)( 3,29)( 4,30)( 5,31)( 6,32)( 7,33)( 8,34)( 9,35)(10,36)
(11,37)(12,38)(13,39)(14,40)(15,41)(16,42)(17,43)(18,44)(19,45)(20,46)(21,47)
(22,48)(23,49)(24,50)(25,51)(26,52);;
s3 := (53,54);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
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(54)!( 2,13)( 3,12)( 4,11)( 5,10)( 6, 9)( 7, 8)(15,26)(16,25)(17,24)
(18,23)(19,22)(20,21)(28,39)(29,38)(30,37)(31,36)(32,35)(33,34)(41,52)(42,51)
(43,50)(44,49)(45,48)(46,47);
s1 := Sym(54)!( 1, 2)( 3,13)( 4,12)( 5,11)( 6,10)( 7, 9)(14,15)(16,26)(17,25)
(18,24)(19,23)(20,22)(27,41)(28,40)(29,52)(30,51)(31,50)(32,49)(33,48)(34,47)
(35,46)(36,45)(37,44)(38,43)(39,42);
s2 := Sym(54)!( 1,27)( 2,28)( 3,29)( 4,30)( 5,31)( 6,32)( 7,33)( 8,34)( 9,35)
(10,36)(11,37)(12,38)(13,39)(14,40)(15,41)(16,42)(17,43)(18,44)(19,45)(20,46)
(21,47)(22,48)(23,49)(24,50)(25,51)(26,52);
s3 := Sym(54)!(53,54);
poly := sub<Sym(54)|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, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, 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 >;

to this polytope