Polytope of Type {12,2,18}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,2,18}*864
if this polytope has a name.
Group : SmallGroup(864,2438)
Rank : 4
Schlafli Type : {12,2,18}
Number of vertices, edges, etc : 12, 12, 18, 18
Order of s₀s₁s₂s₃ : 36
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {12,2,18,2} of size 1728
Vertex Figure Of :
   {2,12,2,18} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,2,9}*432, {6,2,18}*432
   3-fold quotients : {4,2,18}*288, {12,2,6}*288
   4-fold quotients : {3,2,18}*216, {6,2,9}*216
   6-fold quotients : {4,2,9}*144, {2,2,18}*144, {12,2,3}*144, {6,2,6}*144
   8-fold quotients : {3,2,9}*108
   9-fold quotients : {12,2,2}*96, {4,2,6}*96
   12-fold quotients : {2,2,9}*72, {3,2,6}*72, {6,2,3}*72
   18-fold quotients : {4,2,3}*48, {2,2,6}*48, {6,2,2}*48
   24-fold quotients : {3,2,3}*36
   27-fold quotients : {4,2,2}*32
   36-fold quotients : {2,2,3}*24, {3,2,2}*24
   54-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,2,36}*1728, {12,4,18}*1728, {24,2,18}*1728
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 := (15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30);;
s3 := (13,17)(14,15)(16,21)(18,19)(20,25)(22,23)(24,29)(26,27)(28,30);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope