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

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

to this polytope