Polytope of Type {12,2,4,9}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,2,4,9}*1728
if this polytope has a name.
Group : SmallGroup(1728,30229)
Rank : 5
Schlafli Type : {12,2,4,9}
Number of vertices, edges, etc : 12, 12, 4, 18, 9
Order of s₀s₁s₂s₃s₄ : 36
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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) :
   2-fold quotients : {6,2,4,9}*864
   3-fold quotients : {4,2,4,9}*576, {12,2,4,3}*576
   4-fold quotients : {3,2,4,9}*432
   6-fold quotients : {2,2,4,9}*288, {6,2,4,3}*288
   9-fold quotients : {4,2,4,3}*192
   12-fold quotients : {3,2,4,3}*144
   18-fold quotients : {2,2,4,3}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12);;
s1 := ( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12);;
s2 := (14,19)(15,21)(16,23)(17,25)(20,30)(22,32)(26,36)(33,42)(35,44)(37,45)
(39,46)(41,47);;
s3 := (13,14)(15,18)(16,17)(19,27)(20,26)(21,28)(22,24)(23,25)(29,35)(30,36)
(31,33)(32,34)(37,43)(38,44)(39,41)(40,42)(45,48)(46,47);;
s4 := (13,18)(14,16)(15,26)(17,22)(19,23)(20,35)(21,36)(24,31)(25,32)(27,28)
(29,43)(30,44)(33,39)(34,40)(37,41)(38,48)(42,46)(45,47);;
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, 
s1*s2*s1*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*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(48)!( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12);
s1 := Sym(48)!( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12);
s2 := Sym(48)!(14,19)(15,21)(16,23)(17,25)(20,30)(22,32)(26,36)(33,42)(35,44)
(37,45)(39,46)(41,47);
s3 := Sym(48)!(13,14)(15,18)(16,17)(19,27)(20,26)(21,28)(22,24)(23,25)(29,35)
(30,36)(31,33)(32,34)(37,43)(38,44)(39,41)(40,42)(45,48)(46,47);
s4 := Sym(48)!(13,18)(14,16)(15,26)(17,22)(19,23)(20,35)(21,36)(24,31)(25,32)
(27,28)(29,43)(30,44)(33,39)(34,40)(37,41)(38,48)(42,46)(45,47);
poly := sub<Sym(48)|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, s1*s2*s1*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*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope