Polytope of Type {12,6}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope