Polytope of Type {2,12,2,18}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,2,18}*1728
if this polytope has a name.
Group : SmallGroup(1728,30763)
Rank : 5
Schlafli Type : {2,12,2,18}
Number of vertices, edges, etc : 2, 12, 12, 18, 18
Order of s₀s₁s₂s₃s₄ : 36
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   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 : {2,12,2,9}*864, {2,6,2,18}*864
   3-fold quotients : {2,4,2,18}*576, {2,12,2,6}*576
   4-fold quotients : {2,3,2,18}*432, {2,6,2,9}*432
   6-fold quotients : {2,4,2,9}*288, {2,2,2,18}*288, {2,12,2,3}*288, {2,6,2,6}*288
   8-fold quotients : {2,3,2,9}*216
   9-fold quotients : {2,12,2,2}*192, {2,4,2,6}*192
   12-fold quotients : {2,2,2,9}*144, {2,3,2,6}*144, {2,6,2,3}*144
   18-fold quotients : {2,4,2,3}*96, {2,2,2,6}*96, {2,6,2,2}*96
   24-fold quotients : {2,3,2,3}*72
   27-fold quotients : {2,4,2,2}*64
   36-fold quotients : {2,2,2,3}*48, {2,3,2,2}*48
   54-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope