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Polytope of Type {3,2,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,12}*144
if this polytope has a name.
Group : SmallGroup(144,144)
Rank : 4
Schlafli Type : {3,2,12}
Number of vertices, edges, etc : 3, 3, 12, 12
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,12,2} of size 288
   {3,2,12,4} of size 576
   {3,2,12,4} of size 576
   {3,2,12,4} of size 576
   {3,2,12,3} of size 576
   {3,2,12,6} of size 864
   {3,2,12,6} of size 864
   {3,2,12,6} of size 864
   {3,2,12,3} of size 864
   {3,2,12,6} of size 864
   {3,2,12,8} of size 1152
   {3,2,12,8} of size 1152
   {3,2,12,4} of size 1152
   {3,2,12,4} of size 1152
   {3,2,12,4} of size 1152
   {3,2,12,6} of size 1152
   {3,2,12,6} of size 1152
   {3,2,12,4} of size 1296
   {3,2,12,6} of size 1296
   {3,2,12,6} of size 1296
   {3,2,12,6} of size 1296
   {3,2,12,10} of size 1440
   {3,2,12,12} of size 1728
   {3,2,12,12} of size 1728
   {3,2,12,12} of size 1728
   {3,2,12,3} of size 1728
   {3,2,12,4} of size 1728
   {3,2,12,6} of size 1728
   {3,2,12,6} of size 1728
Vertex Figure Of :
   {2,3,2,12} of size 288
   {3,3,2,12} of size 576
   {4,3,2,12} of size 576
   {6,3,2,12} of size 864
   {4,3,2,12} of size 1152
   {6,3,2,12} of size 1152
   {5,3,2,12} of size 1440
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,6}*72
   3-fold quotients : {3,2,4}*48
   4-fold quotients : {3,2,3}*36
   6-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,24}*288, {6,2,12}*288
   3-fold covers : {3,2,36}*432, {9,2,12}*432, {3,6,12}*432a, {3,6,12}*432b
   4-fold covers : {3,2,48}*576, {12,2,12}*576, {6,4,12}*576, {6,2,24}*576, {3,4,12}*576
   5-fold covers : {15,2,12}*720, {3,2,60}*720
   6-fold covers : {3,2,72}*864, {9,2,24}*864, {3,6,24}*864a, {6,2,36}*864, {18,2,12}*864, {6,6,12}*864a, {3,6,24}*864b, {6,6,12}*864b, {6,6,12}*864c, {6,6,12}*864e
   7-fold covers : {21,2,12}*1008, {3,2,84}*1008
   8-fold covers : {3,2,96}*1152, {12,4,12}*1152, {6,8,12}*1152a, {6,4,24}*1152a, {6,8,12}*1152b, {6,4,24}*1152b, {6,4,12}*1152a, {12,2,24}*1152, {24,2,12}*1152, {6,2,48}*1152, {3,8,12}*1152, {3,4,24}*1152, {6,4,12}*1152b, {6,4,12}*1152c
   9-fold covers : {9,2,36}*1296, {9,6,12}*1296a, {3,6,36}*1296a, {27,2,12}*1296, {3,2,108}*1296, {3,6,12}*1296a, {3,6,12}*1296b, {3,6,36}*1296b, {9,6,12}*1296b, {3,6,12}*1296c, {3,6,12}*1296d, {3,6,12}*1296e, {3,6,12}*1296f
   10-fold covers : {15,2,24}*1440, {3,2,120}*1440, {6,10,12}*1440, {30,2,12}*1440, {6,2,60}*1440
   11-fold covers : {33,2,12}*1584, {3,2,132}*1584
   12-fold covers : {3,2,144}*1728, {9,2,48}*1728, {3,6,48}*1728a, {12,2,36}*1728, {36,2,12}*1728, {12,6,12}*1728a, {18,4,12}*1728, {6,4,36}*1728, {6,12,12}*1728a, {6,2,72}*1728, {18,2,24}*1728, {6,6,24}*1728a, {3,6,48}*1728b, {3,4,36}*1728, {9,4,12}*1728, {3,12,12}*1728a, {6,6,24}*1728b, {6,6,24}*1728c, {6,6,24}*1728e, {12,6,12}*1728b, {12,6,12}*1728e, {12,6,12}*1728f, {6,12,12}*1728b, {6,12,12}*1728c, {6,12,12}*1728g, {3,6,12}*1728, {3,12,12}*1728b
   13-fold covers : {39,2,12}*1872, {3,2,156}*1872
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := ( 5, 6)( 7, 8)(10,13)(11,12)(14,15);;
s3 := ( 4,10)( 5, 7)( 6,14)( 8,11)( 9,12)(13,15);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(15)!(2,3);
s1 := Sym(15)!(1,2);
s2 := Sym(15)!( 5, 6)( 7, 8)(10,13)(11,12)(14,15);
s3 := Sym(15)!( 4,10)( 5, 7)( 6,14)( 8,11)( 9,12)(13,15);
poly := sub<Sym(15)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope