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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,4,6}*1728b
if this polytope has a name.
Group : SmallGroup(1728,47887)
Rank : 5
Schlafli Type : {2,6,4,6}
Number of vertices, edges, etc : 2, 18, 36, 36, 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 : {2,6,4,6}*864a
   3-fold quotients : {2,6,4,2}*576
   6-fold quotients : {2,6,4,2}*288
   9-fold quotients : {2,2,4,6}*192a
   18-fold quotients : {2,2,2,6}*96
   27-fold quotients : {2,2,4,2}*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 := ( 3,30)( 4,31)( 5,32)( 6,36)( 7,37)( 8,38)( 9,33)(10,34)(11,35)(12,48)
(13,49)(14,50)(15,54)(16,55)(17,56)(18,51)(19,52)(20,53)(21,39)(22,40)(23,41)
(24,45)(25,46)(26,47)(27,42)(28,43)(29,44);;
s2 := ( 3,12)( 4,13)( 5,14)( 6,15)( 7,16)( 8,17)( 9,18)(10,19)(11,20)(30,39)
(31,40)(32,41)(33,42)(34,43)(35,44)(36,45)(37,46)(38,47);;
s3 := ( 4, 5)( 6,12)( 7,14)( 8,13)( 9,21)(10,23)(11,22)(16,17)(18,24)(19,26)
(20,25)(28,29)(31,32)(33,39)(34,41)(35,40)(36,48)(37,50)(38,49)(43,44)(45,51)
(46,53)(47,52)(55,56);;
s4 := ( 3, 4)( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)
(33,34)(36,37)(39,40)(42,43)(45,46)(48,49)(51,52)(54,55);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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)!( 3,30)( 4,31)( 5,32)( 6,36)( 7,37)( 8,38)( 9,33)(10,34)(11,35)
(12,48)(13,49)(14,50)(15,54)(16,55)(17,56)(18,51)(19,52)(20,53)(21,39)(22,40)
(23,41)(24,45)(25,46)(26,47)(27,42)(28,43)(29,44);
s2 := Sym(56)!( 3,12)( 4,13)( 5,14)( 6,15)( 7,16)( 8,17)( 9,18)(10,19)(11,20)
(30,39)(31,40)(32,41)(33,42)(34,43)(35,44)(36,45)(37,46)(38,47);
s3 := Sym(56)!( 4, 5)( 6,12)( 7,14)( 8,13)( 9,21)(10,23)(11,22)(16,17)(18,24)
(19,26)(20,25)(28,29)(31,32)(33,39)(34,41)(35,40)(36,48)(37,50)(38,49)(43,44)
(45,51)(46,53)(47,52)(55,56);
s4 := Sym(56)!( 3, 4)( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)
(30,31)(33,34)(36,37)(39,40)(42,43)(45,46)(48,49)(51,52)(54,55);
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, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope