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Polytope of Type {12,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6,2}*432c
if this polytope has a name.
Group : SmallGroup(432,756)
Rank : 4
Schlafli Type : {12,6,2}
Number of vertices, edges, etc : 18, 54, 9, 2
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {12,6,2,2} of size 864
   {12,6,2,3} of size 1296
   {12,6,2,4} of size 1728
Vertex Figure Of :
   {2,12,6,2} of size 864
   {4,12,6,2} of size 1728
   {4,12,6,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {4,6,2}*144
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,6,2}*864i
   3-fold covers : {36,6,2}*1296a, {12,6,2}*1296, {36,6,2}*1296b, {36,6,2}*1296c
   4-fold covers : {24,6,2}*1728h, {12,6,4}*1728n, {12,12,2}*1728k, {12,12,2}*1728n
Permutation Representation (GAP) :
s0 := ( 2, 3)( 5, 6)( 8, 9)(11,12)(13,16)(14,18)(15,17);;
s1 := ( 1,11)( 2,10)( 3,12)( 4,14)( 5,13)( 6,15)( 7,17)( 8,16)( 9,18);;
s2 := ( 1, 4)( 2, 5)( 3, 6)(13,16)(14,17)(15,18);;
s3 := (19,20);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(20)!( 2, 3)( 5, 6)( 8, 9)(11,12)(13,16)(14,18)(15,17);
s1 := Sym(20)!( 1,11)( 2,10)( 3,12)( 4,14)( 5,13)( 6,15)( 7,17)( 8,16)( 9,18);
s2 := Sym(20)!( 1, 4)( 2, 5)( 3, 6)(13,16)(14,17)(15,18);
s3 := Sym(20)!(19,20);
poly := sub<Sym(20)|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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2 >; 
 

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