Polytope of Type {6,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12}*144d
if this polytope has a name.
Group : SmallGroup(144,183)
Rank : 3
Schlafli Type : {6,12}
Number of vertices, edges, etc : 6, 36, 12
Order of s₀s₁s₂ : 3
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {6,12,2} of size 288
   {6,12,4} of size 576
   {6,12,6} of size 864
   {6,12,4} of size 1152
   {6,12,4} of size 1152
   {6,12,6} of size 1152
Vertex Figure Of :
   {2,6,12} of size 288
   {4,6,12} of size 576
   {6,6,12} of size 864
   {4,6,12} of size 1152
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {6,4}*48b
   6-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,12}*288a
   3-fold covers : {6,36}*432c, {18,12}*432c, {6,12}*432d
   4-fold covers : {6,24}*576a, {12,12}*576d, {6,12}*576b, {6,24}*576c, {6,24}*576e, {12,12}*576j, {12,12}*576l
   5-fold covers : {30,12}*720d, {6,60}*720d
   6-fold covers : {6,36}*864, {18,12}*864a, {6,12}*864b, {6,12}*864c
   7-fold covers : {42,12}*1008d, {6,84}*1008d
   8-fold covers : {12,24}*1152g, {12,24}*1152h, {6,24}*1152c, {12,24}*1152i, {12,24}*1152k, {6,24}*1152d, {6,12}*1152b, {6,24}*1152e, {24,12}*1152o, {24,12}*1152q, {6,24}*1152h, {6,12}*1152d, {12,12}*1152h, {12,12}*1152k, {12,24}*1152u, {12,24}*1152v, {24,12}*1152w, {24,12}*1152x, {12,24}*1152y, {12,24}*1152z, {24,12}*1152y, {24,12}*1152z, {12,12}*1152t
   9-fold covers : {6,108}*1296c, {54,12}*1296c, {18,36}*1296d, {6,36}*1296i, {6,36}*1296j, {6,36}*1296k, {18,12}*1296i, {18,12}*1296j, {6,12}*1296e, {18,12}*1296k, {6,12}*1296f
   10-fold covers : {30,12}*1440a, {6,60}*1440d
   11-fold covers : {66,12}*1584d, {6,132}*1584d
   12-fold covers : {6,72}*1728a, {18,24}*1728a, {6,24}*1728a, {12,36}*1728c, {6,36}*1728b, {6,72}*1728b, {6,72}*1728c, {12,36}*1728d, {36,12}*1728e, {18,12}*1728c, {12,12}*1728j, {6,12}*1728b, {18,24}*1728c, {6,24}*1728c, {18,24}*1728e, {6,24}*1728e, {36,12}*1728h, {12,12}*1728o, {12,36}*1728i, {36,12}*1728i, {12,12}*1728u, {6,24}*1728f, {6,24}*1728g, {12,12}*1728v, {6,12}*1728i, {12,12}*1728x
   13-fold covers : {78,12}*1872d, {6,156}*1872d
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, 8)( 4, 7)( 9,10)(11,12);;
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, s0*s1*s2*s0*s1*s2*s0*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*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, 8)( 4, 7)( 9,10)(11,12);
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, s0*s1*s2*s0*s1*s2*s0*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 >;

References : None.
to this polytope