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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6,3,4}*864b
if this polytope has a name.
Group : SmallGroup(864,4673)
Rank : 5
Schlafli Type : {6,6,3,4}
Number of vertices, edges, etc : 6, 18, 9, 6, 4
Order of s₀s₁s₂s₃s₄ : 6
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,6,3,4,2} of size 1728
Vertex Figure Of :
   {2,6,6,3,4} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,6,3,4}*288, {6,2,3,4}*288
   6-fold quotients : {3,2,3,4}*144
   9-fold quotients : {2,2,3,4}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,6,3,4}*1728b, {6,6,3,4}*1728b, {6,6,6,4}*1728k, {6,6,6,4}*1728l
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope