Polytope of Type {2,2,52}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,52}*416
if this polytope has a name.
Group : SmallGroup(416,214)
Rank : 4
Schlafli Type : {2,2,52}
Number of vertices, edges, etc : 2, 2, 52, 52
Order of s₀s₁s₂s₃ : 52
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,52,2} of size 832
   {2,2,52,4} of size 1664
Vertex Figure Of :
   {2,2,2,52} of size 832
   {3,2,2,52} of size 1248
   {4,2,2,52} of size 1664
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,26}*208
   4-fold quotients : {2,2,13}*104
   13-fold quotients : {2,2,4}*32
   26-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,52}*832, {4,2,52}*832, {2,2,104}*832
   3-fold covers : {2,6,52}*1248a, {6,2,52}*1248, {2,2,156}*1248
   4-fold covers : {4,4,52}*1664, {2,8,52}*1664a, {2,4,104}*1664a, {2,8,52}*1664b, {2,4,104}*1664b, {2,4,52}*1664, {8,2,52}*1664, {4,2,104}*1664, {2,2,208}*1664
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 7)( 8, 9)(11,14)(12,13)(15,16)(17,18)(19,22)(20,21)(23,24)(25,26)
(27,30)(28,29)(31,32)(33,34)(35,38)(36,37)(39,40)(41,42)(43,46)(44,45)(47,48)
(49,50)(51,54)(52,53)(55,56);;
s3 := ( 5,11)( 6, 8)( 7,17)( 9,19)(10,13)(12,15)(14,25)(16,27)(18,21)(20,23)
(22,33)(24,35)(26,29)(28,31)(30,41)(32,43)(34,37)(36,39)(38,49)(40,51)(42,45)
(44,47)(46,55)(48,52)(50,53)(54,56);;
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*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(56)!(1,2);
s1 := Sym(56)!(3,4);
s2 := Sym(56)!( 6, 7)( 8, 9)(11,14)(12,13)(15,16)(17,18)(19,22)(20,21)(23,24)
(25,26)(27,30)(28,29)(31,32)(33,34)(35,38)(36,37)(39,40)(41,42)(43,46)(44,45)
(47,48)(49,50)(51,54)(52,53)(55,56);
s3 := Sym(56)!( 5,11)( 6, 8)( 7,17)( 9,19)(10,13)(12,15)(14,25)(16,27)(18,21)
(20,23)(22,33)(24,35)(26,29)(28,31)(30,41)(32,43)(34,37)(36,39)(38,49)(40,51)
(42,45)(44,47)(46,55)(48,52)(50,53)(54,56);
poly := sub<Sym(56)|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*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 >;

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