Polytope of Type {6,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,3}*144
Also Known As : {6,3}_(2,2). if this polytope has another name.
Group : SmallGroup(144,183)
Rank : 3
Schlafli Type : {6,3}
Number of vertices, edges, etc : 24, 36, 12
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Toroidal
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {6,3,2} of size 288
   {6,3,4} of size 576
   {6,3,3} of size 720
   {6,3,6} of size 864
   {6,3,4} of size 1152
   {6,3,4} of size 1152
   {6,3,6} of size 1440
Vertex Figure Of :
   {2,6,3} of size 288
   {4,6,3} of size 576
   {3,6,3} of size 720
   {6,6,3} of size 864
   {4,6,3} of size 1152
   {8,6,3} of size 1152
   {4,6,3} of size 1152
   {6,6,3} of size 1440
   {10,6,3} of size 1440
   {12,6,3} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {6,3}*48
   4-fold quotients : {6,3}*36
   6-fold quotients : {3,3}*24
   12-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,3}*288, {6,6}*288a
   3-fold covers : {6,9}*432, {6,3}*432
   4-fold covers : {6,3}*576, {6,12}*576a, {12,6}*576c, {6,6}*576a, {6,12}*576d, {12,6}*576e, {12,3}*576
   5-fold covers : {6,15}*720e
   6-fold covers : {12,9}*864, {12,3}*864, {6,18}*864, {6,6}*864b, {6,6}*864c
   7-fold covers : {6,21}*1008b
   8-fold covers : {12,3}*1152a, {6,6}*1152b, {12,12}*1152d, {12,12}*1152f, {6,12}*1152a, {6,6}*1152c, {6,6}*1152e, {6,24}*1152g, {6,24}*1152i, {12,12}*1152j, {24,6}*1152j, {12,6}*1152e, {12,12}*1152p, {24,6}*1152m, {12,3}*1152b, {12,6}*1152g, {24,3}*1152b, {24,3}*1152c, {12,6}*1152j
   9-fold covers : {6,27}*1296, {18,9}*1296a, {6,9}*1296a, {6,3}*1296, {6,9}*1296b, {18,3}*1296a, {6,9}*1296c, {6,9}*1296d
   10-fold covers : {12,15}*1440c, {30,6}*1440g, {6,30}*1440h
   11-fold covers : {6,33}*1584
   12-fold covers : {6,9}*1728, {6,3}*1728, {6,36}*1728a, {12,18}*1728a, {6,18}*1728a, {6,36}*1728c, {12,18}*1728b, {6,12}*1728a, {12,6}*1728c, {6,6}*1728a, {6,12}*1728d, {12,6}*1728e, {12,9}*1728, {12,3}*1728, {6,12}*1728g, {12,6}*1728g, {6,6}*1728f, {6,12}*1728h, {12,6}*1728h
   13-fold covers : {6,39}*1872
Permutation Representation (GAP) :

s0 := ( 3, 4)( 7, 8)(11,12);;
s1 := ( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12);;
s2 := ( 1, 6)( 2, 5)( 3, 7)( 4, 8)( 9,10);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1 >;

References : None.
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