Polytope of Type {2,6,6,3,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,6,3,4}*1728b
if this polytope has a name.
Group : SmallGroup(1728,47874)
Rank : 6
Schlafli Type : {2,6,6,3,4}
Number of vertices, edges, etc : 2, 6, 18, 9, 6, 4
Order of s₀s₁s₂s₃s₄s₅ : 6
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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 : {2,2,6,3,4}*576, {2,6,2,3,4}*576
   6-fold quotients : {2,3,2,3,4}*288
   9-fold quotients : {2,2,2,3,4}*192
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 7,11)( 8,12)( 9,13)(10,14)(19,23)(20,24)(21,25)(22,26)(31,35)(32,36)
(33,37)(34,38);;
s2 := ( 3, 7)( 4, 8)( 5, 9)( 6,10)(15,31)(16,32)(17,33)(18,34)(19,27)(20,28)
(21,29)(22,30)(23,35)(24,36)(25,37)(26,38);;
s3 := ( 3,15)( 4,17)( 5,16)( 6,18)( 7,19)( 8,21)( 9,20)(10,22)(11,23)(12,25)
(13,24)(14,26)(28,29)(32,33)(36,37);;
s4 := ( 5, 6)( 9,10)(13,14)(15,27)(16,28)(17,30)(18,29)(19,31)(20,32)(21,34)
(22,33)(23,35)(24,36)(25,38)(26,37);;
s5 := ( 3, 6)( 4, 5)( 7,10)( 8, 9)(11,14)(12,13)(15,18)(16,17)(19,22)(20,21)
(23,26)(24,25)(27,30)(28,29)(31,34)(32,33)(35,38)(36,37);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
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, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s3*s4*s3*s4*s3*s4, 
s1*s2*s3*s2*s1*s2*s3*s2, s4*s5*s4*s5*s4*s5*s4*s5, 
s3*s5*s4*s3*s5*s4*s3*s5*s4, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(38)!(1,2);
s1 := Sym(38)!( 7,11)( 8,12)( 9,13)(10,14)(19,23)(20,24)(21,25)(22,26)(31,35)
(32,36)(33,37)(34,38);
s2 := Sym(38)!( 3, 7)( 4, 8)( 5, 9)( 6,10)(15,31)(16,32)(17,33)(18,34)(19,27)
(20,28)(21,29)(22,30)(23,35)(24,36)(25,37)(26,38);
s3 := Sym(38)!( 3,15)( 4,17)( 5,16)( 6,18)( 7,19)( 8,21)( 9,20)(10,22)(11,23)
(12,25)(13,24)(14,26)(28,29)(32,33)(36,37);
s4 := Sym(38)!( 5, 6)( 9,10)(13,14)(15,27)(16,28)(17,30)(18,29)(19,31)(20,32)
(21,34)(22,33)(23,35)(24,36)(25,38)(26,37);
s5 := Sym(38)!( 3, 6)( 4, 5)( 7,10)( 8, 9)(11,14)(12,13)(15,18)(16,17)(19,22)
(20,21)(23,26)(24,25)(27,30)(28,29)(31,34)(32,33)(35,38)(36,37);
poly := sub<Sym(38)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, 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, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s3*s4*s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2, 
s4*s5*s4*s5*s4*s5*s4*s5, s3*s5*s4*s3*s5*s4*s3*s5*s4, 
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope