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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,6,2}*1728b
if this polytope has a name.
Group : SmallGroup(1728,47887)
Rank : 5
Schlafli Type : {4,4,6,2}
Number of vertices, edges, etc : 18, 36, 54, 6, 2
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 : {4,4,2,2}*576
   6-fold quotients : {4,4,2,2}*288
   18-fold quotients : {2,2,6,2}*96
   36-fold quotients : {2,2,3,2}*48
   54-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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