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

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

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