Polytope of Type {2,6,3,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,3,2}*144
if this polytope has a name.
Group : SmallGroup(144,192)
Rank : 5
Schlafli Type : {2,6,3,2}
Number of vertices, edges, etc : 2, 6, 9, 3, 2
Order of s₀s₁s₂s₃s₄ : 6
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,3,2,2} of size 288
   {2,6,3,2,3} of size 432
   {2,6,3,2,4} of size 576
   {2,6,3,2,5} of size 720
   {2,6,3,2,6} of size 864
   {2,6,3,2,7} of size 1008
   {2,6,3,2,8} of size 1152
   {2,6,3,2,9} of size 1296
   {2,6,3,2,10} of size 1440
   {2,6,3,2,11} of size 1584
   {2,6,3,2,12} of size 1728
   {2,6,3,2,13} of size 1872
Vertex Figure Of :
   {2,2,6,3,2} of size 288
   {3,2,6,3,2} of size 432
   {4,2,6,3,2} of size 576
   {5,2,6,3,2} of size 720
   {6,2,6,3,2} of size 864
   {7,2,6,3,2} of size 1008
   {8,2,6,3,2} of size 1152
   {9,2,6,3,2} of size 1296
   {10,2,6,3,2} of size 1440
   {11,2,6,3,2} of size 1584
   {12,2,6,3,2} of size 1728
   {13,2,6,3,2} of size 1872
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,2,3,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,6,3,2}*288, {2,6,6,2}*288b
   3-fold covers : {2,6,9,2}*432, {2,6,3,2}*432, {2,6,3,6}*432, {6,6,3,2}*432b
   4-fold covers : {8,6,3,2}*576, {2,6,12,2}*576b, {2,6,6,4}*576b, {2,12,6,2}*576c, {4,6,6,2}*576c, {2,6,3,2}*576, {2,6,3,4}*576, {2,12,3,2}*576
   5-fold covers : {10,6,3,2}*720, {2,6,15,2}*720
   6-fold covers : {4,6,9,2}*864, {4,6,3,2}*864a, {2,6,18,2}*864b, {2,6,6,2}*864a, {12,6,3,2}*864b, {4,6,3,6}*864, {2,6,6,2}*864d, {2,6,6,6}*864d, {2,6,6,6}*864f, {6,6,6,2}*864c
   7-fold covers : {14,6,3,2}*1008, {2,6,21,2}*1008
   8-fold covers : {16,6,3,2}*1152, {2,6,12,4}*1152b, {4,12,6,2}*1152c, {2,12,12,2}*1152b, {4,6,6,4}*1152c, {2,12,6,4}*1152a, {4,6,12,2}*1152c, {2,6,6,8}*1152b, {2,24,6,2}*1152a, {8,6,6,2}*1152c, {2,6,24,2}*1152c, {2,12,3,2}*1152, {2,24,3,2}*1152, {2,6,3,8}*1152, {4,6,3,4}*1152, {4,6,3,2}*1152a, {4,12,3,2}*1152, {2,6,6,2}*1152a, {2,6,6,4}*1152b, {2,12,6,2}*1152b
   9-fold covers : {2,18,9,2}*1296, {2,6,9,2}*1296a, {2,6,27,2}*1296, {2,6,9,2}*1296b, {2,6,9,2}*1296c, {2,6,9,2}*1296d, {2,6,3,2}*1296, {2,18,3,2}*1296, {2,6,9,6}*1296, {6,6,9,2}*1296b, {18,6,3,2}*1296b, {2,6,3,6}*1296a, {2,6,3,6}*1296b, {6,6,3,2}*1296c, {6,6,3,2}*1296d, {6,6,3,2}*1296e, {6,6,3,6}*1296b
   10-fold covers : {20,6,3,2}*1440, {4,6,15,2}*1440, {2,6,6,10}*1440b, {2,30,6,2}*1440a, {10,6,6,2}*1440b, {2,6,30,2}*1440c
   11-fold covers : {22,6,3,2}*1584, {2,6,33,2}*1584
   12-fold covers : {8,6,9,2}*1728, {8,6,3,2}*1728a, {2,6,36,2}*1728b, {2,6,12,2}*1728a, {2,6,18,4}*1728b, {2,6,6,4}*1728a, {2,12,18,2}*1728b, {4,6,18,2}*1728b, {2,12,6,2}*1728c, {4,6,6,2}*1728c, {24,6,3,2}*1728b, {8,6,3,6}*1728, {2,6,9,2}*1728, {2,6,9,4}*1728, {2,12,9,2}*1728, {2,6,3,2}*1728, {2,6,3,4}*1728, {2,12,3,2}*1728, {2,6,6,12}*1728d, {2,6,12,6}*1728c, {2,6,12,6}*1728e, {6,6,12,2}*1728c, {6,6,6,4}*1728e, {2,6,12,2}*1728g, {2,12,6,2}*1728g, {12,6,6,2}*1728e, {4,6,6,6}*1728g, {4,6,6,6}*1728h, {2,6,6,4}*1728h, {2,6,6,12}*1728g, {2,12,6,6}*1728f, {2,12,6,6}*1728g, {4,6,6,2}*1728h, {6,12,6,2}*1728g, {6,6,3,4}*1728b, {2,6,3,6}*1728a, {2,6,3,6}*1728b, {2,6,3,12}*1728, {2,12,3,6}*1728, {6,6,3,2}*1728, {6,12,3,2}*1728b
   13-fold covers : {26,6,3,2}*1872, {2,6,39,2}*1872
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 6, 7)( 8, 9)(10,11);;
s2 := ( 3, 6)( 4,10)( 5, 8)( 9,11);;
s3 := ( 3, 4)( 6, 9)( 7, 8)(10,11);;
s4 := (12,13);;
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*s1*s0*s1, 
s0*s2*s0*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, s2*s3*s2*s3*s2*s3, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(13)!(1,2);
s1 := Sym(13)!( 6, 7)( 8, 9)(10,11);
s2 := Sym(13)!( 3, 6)( 4,10)( 5, 8)( 9,11);
s3 := Sym(13)!( 3, 4)( 6, 9)( 7, 8)(10,11);
s4 := Sym(13)!(12,13);
poly := sub<Sym(13)|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*s1*s0*s1, s0*s2*s0*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, 
s2*s3*s2*s3*s2*s3, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2 >;

to this polytope