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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,2,18,2}*1728
if this polytope has a name.
Group : SmallGroup(1728,30763)
Rank : 5
Schlafli Type : {12,2,18,2}
Number of vertices, edges, etc : 12, 12, 18, 18, 2
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 : {12,2,9,2}*864, {6,2,18,2}*864
   3-fold quotients : {4,2,18,2}*576, {12,2,6,2}*576
   4-fold quotients : {3,2,18,2}*432, {6,2,9,2}*432
   6-fold quotients : {4,2,9,2}*288, {2,2,18,2}*288, {12,2,3,2}*288, {6,2,6,2}*288
   8-fold quotients : {3,2,9,2}*216
   9-fold quotients : {12,2,2,2}*192, {4,2,6,2}*192
   12-fold quotients : {2,2,9,2}*144, {3,2,6,2}*144, {6,2,3,2}*144
   18-fold quotients : {4,2,3,2}*96, {2,2,6,2}*96, {6,2,2,2}*96
   24-fold quotients : {3,2,3,2}*72
   27-fold quotients : {4,2,2,2}*64
   36-fold quotients : {2,2,3,2}*48, {3,2,2,2}*48
   54-fold quotients : {2,2,2,2}*32
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 := (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);;
s4 := (31,32);;
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*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, 
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, 
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(32)!( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12);
s1 := Sym(32)!( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12);
s2 := Sym(32)!(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30);
s3 := Sym(32)!(13,17)(14,15)(16,21)(18,19)(20,25)(22,23)(24,29)(26,27)(28,30);
s4 := Sym(32)!(31,32);
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*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, 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, 
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 >; 
 

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