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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,4,6}*1728b
if this polytope has a name.
Group : SmallGroup(1728,47887)
Rank : 5
Schlafli Type : {2,4,4,6}
Number of vertices, edges, etc : 2, 18, 36, 54, 6
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 : {2,4,4,2}*576
   6-fold quotients : {2,4,4,2}*288
   18-fold quotients : {2,2,2,6}*96
   36-fold quotients : {2,2,2,3}*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 := ( 6,12)( 7,13)( 8,14)( 9,21)(10,22)(11,23)(18,24)(19,25)(20,26)(33,39)
(34,40)(35,41)(36,48)(37,49)(38,50)(45,51)(46,52)(47,53);;
s2 := (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);;
s3 := ( 3,15)( 4,17)( 5,16)( 7, 8)( 9,24)(10,26)(11,25)(13,14)(18,21)(19,23)
(20,22)(28,29)(30,42)(31,44)(32,43)(34,35)(36,51)(37,53)(38,52)(40,41)(45,48)
(46,50)(47,49)(55,56);;
s4 := ( 3,31)( 4,30)( 5,32)( 6,34)( 7,33)( 8,35)( 9,37)(10,36)(11,38)(12,40)
(13,39)(14,41)(15,43)(16,42)(17,44)(18,46)(19,45)(20,47)(21,49)(22,48)(23,50)
(24,52)(25,51)(26,53)(27,55)(28,54)(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*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

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