Polytope of Type {12,12,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,12,2}*1728n
if this polytope has a name.
Group : SmallGroup(1728,47870)
Rank : 4
Schlafli Type : {12,12,2}
Number of vertices, edges, etc : 36, 216, 36, 2
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 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) :
   4-fold quotients : {12,6,2}*432c
   9-fold quotients : {12,4,2}*192c
   12-fold quotients : {4,6,2}*144
   18-fold quotients : {6,4,2}*96c
   36-fold quotients : {3,4,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

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

to this polytope