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Polytope of Type {3,2,2,3,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,2,3,2}*144
if this polytope has a name.
Group : SmallGroup(144,192)
Rank : 6
Schlafli Type : {3,2,2,3,2}
Number of vertices, edges, etc : 3, 3, 2, 3, 3, 2
Order of s0s1s2s3s4s5 : 6
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,2,3,2,2} of size 288
   {3,2,2,3,2,3} of size 432
   {3,2,2,3,2,4} of size 576
   {3,2,2,3,2,5} of size 720
   {3,2,2,3,2,6} of size 864
   {3,2,2,3,2,7} of size 1008
   {3,2,2,3,2,8} of size 1152
   {3,2,2,3,2,9} of size 1296
   {3,2,2,3,2,10} of size 1440
   {3,2,2,3,2,11} of size 1584
   {3,2,2,3,2,12} of size 1728
   {3,2,2,3,2,13} of size 1872
Vertex Figure Of :
   {2,3,2,2,3,2} of size 288
   {3,3,2,2,3,2} of size 576
   {4,3,2,2,3,2} of size 576
   {6,3,2,2,3,2} of size 864
   {4,3,2,2,3,2} of size 1152
   {6,3,2,2,3,2} of size 1152
   {5,3,2,2,3,2} of size 1440
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,2,6,2}*288, {6,2,2,3,2}*288
   3-fold covers : {3,2,2,9,2}*432, {9,2,2,3,2}*432, {3,2,2,3,6}*432, {3,2,6,3,2}*432, {3,6,2,3,2}*432
   4-fold covers : {3,2,2,12,2}*576, {12,2,2,3,2}*576, {3,2,2,6,4}*576a, {3,2,4,6,2}*576a, {6,4,2,3,2}*576a, {3,2,2,3,4}*576, {3,2,4,3,2}*576, {3,4,2,3,2}*576, {6,2,2,6,2}*576
   5-fold covers : {3,2,2,15,2}*720, {15,2,2,3,2}*720
   6-fold covers : {3,2,2,18,2}*864, {6,2,2,9,2}*864, {9,2,2,6,2}*864, {18,2,2,3,2}*864, {3,2,2,6,6}*864a, {3,2,2,6,6}*864c, {3,2,6,6,2}*864a, {3,2,6,6,2}*864b, {3,6,2,6,2}*864, {6,2,2,3,6}*864, {6,2,6,3,2}*864, {6,6,2,3,2}*864a, {6,6,2,3,2}*864c
   7-fold covers : {3,2,2,21,2}*1008, {21,2,2,3,2}*1008
   8-fold covers : {3,2,2,12,4}*1152a, {3,2,4,12,2}*1152a, {12,4,2,3,2}*1152a, {3,2,4,6,4}*1152a, {3,2,2,6,8}*1152, {3,2,8,6,2}*1152, {6,8,2,3,2}*1152, {3,2,2,24,2}*1152, {24,2,2,3,2}*1152, {6,2,2,6,4}*1152a, {6,2,4,6,2}*1152a, {6,4,2,6,2}*1152a, {6,2,2,12,2}*1152, {12,2,2,6,2}*1152, {3,2,2,3,8}*1152, {3,2,8,3,2}*1152, {3,8,2,3,2}*1152, {3,2,2,6,4}*1152, {3,2,4,6,2}*1152, {3,4,2,6,2}*1152, {6,2,2,3,4}*1152, {6,2,4,3,2}*1152, {6,4,2,3,2}*1152
   9-fold covers : {9,2,2,9,2}*1296, {3,2,2,27,2}*1296, {27,2,2,3,2}*1296, {3,2,2,9,6}*1296, {3,2,6,9,2}*1296, {3,6,2,9,2}*1296, {9,2,2,3,6}*1296, {9,2,6,3,2}*1296, {9,6,2,3,2}*1296, {3,2,2,3,6}*1296, {3,2,6,3,2}*1296, {3,6,2,3,2}*1296, {3,2,6,3,6}*1296, {3,6,2,3,6}*1296, {3,6,6,3,2}*1296
   10-fold covers : {3,2,2,6,10}*1440, {3,2,10,6,2}*1440, {6,10,2,3,2}*1440, {3,2,2,30,2}*1440, {6,2,2,15,2}*1440, {15,2,2,6,2}*1440, {30,2,2,3,2}*1440
   11-fold covers : {3,2,2,33,2}*1584, {33,2,2,3,2}*1584
   12-fold covers : {9,2,2,12,2}*1728, {12,2,2,9,2}*1728, {3,2,2,36,2}*1728, {36,2,2,3,2}*1728, {3,2,2,18,4}*1728a, {3,2,4,18,2}*1728a, {6,4,2,9,2}*1728a, {9,2,2,6,4}*1728a, {9,2,4,6,2}*1728a, {18,4,2,3,2}*1728a, {3,4,2,9,2}*1728, {9,2,2,3,4}*1728, {9,2,4,3,2}*1728, {3,2,2,9,4}*1728, {3,2,4,9,2}*1728, {9,4,2,3,2}*1728, {6,2,2,18,2}*1728, {18,2,2,6,2}*1728, {3,2,2,6,12}*1728a, {3,2,2,12,6}*1728a, {3,2,2,12,6}*1728b, {3,2,6,12,2}*1728a, {3,2,6,12,2}*1728b, {3,2,12,6,2}*1728a, {3,6,2,12,2}*1728, {6,12,2,3,2}*1728a, {12,2,2,3,6}*1728, {12,2,6,3,2}*1728, {12,6,2,3,2}*1728a, {12,6,2,3,2}*1728b, {3,2,4,6,6}*1728a, {3,2,4,6,6}*1728b, {3,2,6,6,4}*1728a, {3,2,6,6,4}*1728b, {3,6,2,6,4}*1728a, {6,4,2,3,6}*1728a, {3,2,2,6,12}*1728c, {3,2,12,6,2}*1728c, {3,6,4,6,2}*1728, {6,4,6,3,2}*1728, {6,12,2,3,2}*1728c, {3,2,2,3,6}*1728, {3,2,2,3,12}*1728, {3,2,4,3,6}*1728, {3,2,6,3,2}*1728, {3,2,6,3,4}*1728, {3,2,12,3,2}*1728, {3,4,2,3,6}*1728, {3,4,6,3,2}*1728, {3,6,2,3,2}*1728, {3,6,2,3,4}*1728, {3,6,4,3,2}*1728, {3,12,2,3,2}*1728, {6,2,2,6,6}*1728a, {6,2,2,6,6}*1728c, {6,2,6,6,2}*1728a, {6,2,6,6,2}*1728b, {6,6,2,6,2}*1728a, {6,6,2,6,2}*1728c
   13-fold covers : {3,2,2,39,2}*1872, {39,2,2,3,2}*1872
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := (4,5);;
s3 := (7,8);;
s4 := (6,7);;
s5 := ( 9,10);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(10)!(2,3);
s1 := Sym(10)!(1,2);
s2 := Sym(10)!(4,5);
s3 := Sym(10)!(7,8);
s4 := Sym(10)!(6,7);
s5 := Sym(10)!( 9,10);
poly := sub<Sym(10)|s0,s1,s2,s3,s4,s5>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5, s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4 >; 
 

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