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

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

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

Permutation Representation (Magma) :

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

to this polytope