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Polytope of Type {4,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12}*288
if this polytope has a name.
Group : SmallGroup(288,889)
Rank : 3
Schlafli Type : {4,12}
Number of vertices, edges, etc : 12, 72, 36
Order of s0s1s2 : 4
Order of s0s1s2s1 : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {4,12,2} of size 576
   {4,12,4} of size 1152
   {4,12,6} of size 1728
   {4,12,6} of size 1728
   {4,12,3} of size 1728
Vertex Figure Of :
   {2,4,12} of size 576
   {4,4,12} of size 1152
   {6,4,12} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,6}*144
   4-fold quotients : {4,6}*72
   9-fold quotients : {4,4}*32
   18-fold quotients : {2,4}*16, {4,2}*16
   36-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,12}*576, {8,12}*576a, {4,24}*576a, {4,24}*576b, {8,12}*576b
   3-fold covers : {4,12}*864b, {12,12}*864d, {12,12}*864e, {4,12}*864c, {12,12}*864i, {12,12}*864k
   4-fold covers : {4,24}*1152a, {8,12}*1152a, {8,24}*1152a, {8,24}*1152b, {8,24}*1152c, {8,24}*1152d, {4,48}*1152a, {16,12}*1152a, {4,48}*1152b, {16,12}*1152b, {4,12}*1152a, {8,12}*1152b, {4,24}*1152b
   5-fold covers : {4,60}*1440, {20,12}*1440
   6-fold covers : {4,12}*1728a, {12,12}*1728d, {12,12}*1728e, {8,12}*1728a, {24,12}*1728g, {24,12}*1728h, {4,24}*1728a, {12,24}*1728i, {12,24}*1728j, {4,24}*1728c, {12,24}*1728k, {12,24}*1728l, {8,12}*1728d, {24,12}*1728m, {24,12}*1728n, {4,24}*1728e, {12,24}*1728q, {4,24}*1728g, {12,24}*1728r, {8,12}*1728g, {24,12}*1728s, {8,12}*1728h, {24,12}*1728t, {4,12}*1728c, {12,12}*1728r, {12,12}*1728s, {24,12}*1728u, {12,24}*1728v, {12,24}*1728w, {24,12}*1728x
Permutation Representation (GAP) :
s0 := ( 8, 9)(11,12);;
s1 := ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12);;
s2 := ( 1, 2)( 4, 5)( 7,10)( 8,12)( 9,11);;
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*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*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)!( 8, 9)(11,12);
s1 := Sym(12)!( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12);
s2 := Sym(12)!( 1, 2)( 4, 5)( 7,10)( 8,12)( 9,11);
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*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 >; 
 
References : None.
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