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# Polytope of Type {2,12,6}

Atlas Canonical Name : {2,12,6}*432b
if this polytope has a name.
Group : SmallGroup(432,530)
Rank : 4
Schlafli Type : {2,12,6}
Number of vertices, edges, etc : 2, 18, 54, 9
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,12,6,2} of size 864
Vertex Figure Of :
{2,2,12,6} of size 864
{3,2,12,6} of size 1296
{4,2,12,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {2,4,6}*144
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,12,6}*864b, {2,12,6}*864e
3-fold covers : {6,12,6}*1296d, {2,12,6}*1296
4-fold covers : {8,12,6}*1728a, {2,24,6}*1728d, {4,12,6}*1728h, {2,12,12}*1728d
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 7, 8)(10,11)(13,14)(15,18)(16,20)(17,19);;
s2 := ( 3,13)( 4,12)( 5,14)( 6,19)( 7,18)( 8,20)( 9,16)(10,15)(11,17);;
s3 := ( 3, 6)( 4, 7)( 5, 8)(15,20)(16,18)(17,19);;
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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s2*s1*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :
s0 := Sym(20)!(1,2);
s1 := Sym(20)!( 4, 5)( 7, 8)(10,11)(13,14)(15,18)(16,20)(17,19);
s2 := Sym(20)!( 3,13)( 4,12)( 5,14)( 6,19)( 7,18)( 8,20)( 9,16)(10,15)(11,17);
s3 := Sym(20)!( 3, 6)( 4, 7)( 5, 8)(15,20)(16,18)(17,19);
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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s2*s1*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3 >;

to this polytope