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

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

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

References : None.
to this polytope