Polytope of Type {2,6,4,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,4,4}*1728b
if this polytope has a name.
Group : SmallGroup(1728,47887)
Rank : 5
Schlafli Type : {2,6,4,4}
Number of vertices, edges, etc : 2, 6, 54, 36, 18
Order of s₀s₁s₂s₃s₄ : 6
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,2,4,4}*576
   6-fold quotients : {2,2,4,4}*288
   18-fold quotients : {2,6,2,2}*96
   36-fold quotients : {2,3,2,2}*48
   54-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)
(34,35)(37,38)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56);;
s2 := ( 3, 4)( 6,13)( 7,12)( 8,14)( 9,22)(10,21)(11,23)(15,16)(18,25)(19,24)
(20,26)(27,28)(30,31)(33,40)(34,39)(35,41)(36,49)(37,48)(38,50)(42,43)(45,52)
(46,51)(47,53)(54,55);;
s3 := (12,21)(13,22)(14,23)(15,24)(16,25)(17,26)(18,27)(19,28)(20,29)(39,48)
(40,49)(41,50)(42,51)(43,52)(44,53)(45,54)(46,55)(47,56);;
s4 := ( 3,42)( 4,43)( 5,44)( 6,33)( 7,34)( 8,35)( 9,51)(10,52)(11,53)(12,39)
(13,40)(14,41)(15,30)(16,31)(17,32)(18,48)(19,49)(20,50)(21,45)(22,46)(23,47)
(24,36)(25,37)(26,38)(27,54)(28,55)(29,56);;
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, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(56)!(1,2);
s1 := Sym(56)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)
(31,32)(34,35)(37,38)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56);
s2 := Sym(56)!( 3, 4)( 6,13)( 7,12)( 8,14)( 9,22)(10,21)(11,23)(15,16)(18,25)
(19,24)(20,26)(27,28)(30,31)(33,40)(34,39)(35,41)(36,49)(37,48)(38,50)(42,43)
(45,52)(46,51)(47,53)(54,55);
s3 := Sym(56)!(12,21)(13,22)(14,23)(15,24)(16,25)(17,26)(18,27)(19,28)(20,29)
(39,48)(40,49)(41,50)(42,51)(43,52)(44,53)(45,54)(46,55)(47,56);
s4 := Sym(56)!( 3,42)( 4,43)( 5,44)( 6,33)( 7,34)( 8,35)( 9,51)(10,52)(11,53)
(12,39)(13,40)(14,41)(15,30)(16,31)(17,32)(18,48)(19,49)(20,50)(21,45)(22,46)
(23,47)(24,36)(25,37)(26,38)(27,54)(28,55)(29,56);
poly := sub<Sym(56)|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, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3 >;

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