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Polytope of Type {2,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,4}*144
if this polytope has a name.
Group : SmallGroup(144,186)
Rank : 4
Schlafli Type : {2,6,4}
Number of vertices, edges, etc : 2, 9, 18, 6
Order of s0s1s2s3 : 4
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,4,2} of size 288
   {2,6,4,4} of size 576
   {2,6,4,6} of size 864
   {2,6,4,8} of size 1152
   {2,6,4,10} of size 1440
   {2,6,4,12} of size 1728
Vertex Figure Of :
   {2,2,6,4} of size 288
   {3,2,6,4} of size 432
   {4,2,6,4} of size 576
   {5,2,6,4} of size 720
   {6,2,6,4} of size 864
   {7,2,6,4} of size 1008
   {8,2,6,4} of size 1152
   {9,2,6,4} of size 1296
   {10,2,6,4} of size 1440
   {11,2,6,4} of size 1584
   {12,2,6,4} of size 1728
   {13,2,6,4} of size 1872
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,6,4}*288
   3-fold covers : {2,6,4}*432, {2,6,12}*432a, {2,6,12}*432b, {2,6,12}*432c
   4-fold covers : {2,6,8}*576, {4,6,4}*576b, {2,12,4}*576
   5-fold covers : {2,6,20}*720
   6-fold covers : {2,6,4}*864a, {2,6,12}*864e, {2,6,12}*864f, {6,6,4}*864j, {2,6,4}*864b, {2,6,12}*864h, {2,6,12}*864i
   7-fold covers : {2,6,28}*1008
   8-fold covers : {4,12,4}*1152a, {2,24,4}*1152a, {2,12,8}*1152a, {2,24,4}*1152b, {2,12,8}*1152b, {2,12,4}*1152, {8,6,4}*1152a, {4,6,8}*1152b, {2,6,16}*1152
   9-fold covers : {2,18,4}*1296, {2,6,36}*1296a, {2,6,12}*1296, {2,6,36}*1296b, {2,6,36}*1296c, {6,6,4}*1296d
   10-fold covers : {10,6,4}*1440, {2,30,4}*1440, {2,6,20}*1440
   11-fold covers : {2,6,44}*1584
   12-fold covers : {2,6,8}*1728a, {2,6,24}*1728d, {2,6,24}*1728e, {4,6,4}*1728a, {4,6,12}*1728f, {4,6,12}*1728g, {2,12,4}*1728b, {2,12,12}*1728f, {2,12,12}*1728g, {6,6,8}*1728f, {12,6,4}*1728k, {2,12,4}*1728d, {2,12,12}*1728j, {2,6,8}*1728b, {2,6,24}*1728g, {6,12,4}*1728n, {4,6,4}*1728d, {4,6,12}*1728m, {2,6,24}*1728h, {4,6,12}*1728n, {2,12,12}*1728l, {2,12,12}*1728o
   13-fold covers : {2,6,52}*1872
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (5,6)(7,8);;
s2 := (4,5);;
s3 := (3,4)(5,7)(6,8);;
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, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(8)!(1,2);
s1 := Sym(8)!(5,6)(7,8);
s2 := Sym(8)!(4,5);
s3 := Sym(8)!(3,4)(5,7)(6,8);
poly := sub<Sym(8)|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, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2 >; 
 

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