Polytope of Type {4,26,2}

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

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