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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,6,4}*1728k
if this polytope has a name.
Group : SmallGroup(1728,47887)
Rank : 5
Schlafli Type : {2,6,6,4}
Number of vertices, edges, etc : 2, 6, 54, 36, 12
Order of s₀s₁s₂s₃s₄ : 12
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) :
   2-fold quotients : {2,3,6,4}*864b
   9-fold quotients : {2,6,2,4}*192
   18-fold quotients : {2,3,2,4}*96, {2,6,2,2}*96
   27-fold quotients : {2,2,2,4}*64
   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)( 6, 9)( 7,11)( 8,10)(12,21)(13,23)(14,22)(15,27)(16,29)(17,28)
(18,24)(19,26)(20,25)(31,32)(33,36)(34,38)(35,37)(39,48)(40,50)(41,49)(42,54)
(43,56)(44,55)(45,51)(46,53)(47,52);;
s2 := ( 3,40)( 4,39)( 5,41)( 6,46)( 7,45)( 8,47)( 9,43)(10,42)(11,44)(12,31)
(13,30)(14,32)(15,37)(16,36)(17,38)(18,34)(19,33)(20,35)(21,49)(22,48)(23,50)
(24,55)(25,54)(26,56)(27,52)(28,51)(29,53);;
s3 := ( 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);;
s4 := ( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(24,27)(25,28)(26,29)(33,36)
(34,37)(35,38)(42,45)(43,46)(44,47)(51,54)(52,55)(53,56);;
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, 
s3*s4*s3*s4*s3*s4*s3*s4, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope