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Polytope of Type {2,4,3,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,3,2,2}*192
if this polytope has a name.
Group : SmallGroup(192,1537)
Rank : 6
Schlafli Type : {2,4,3,2,2}
Number of vertices, edges, etc : 2, 4, 6, 3, 2, 2
Order of s0s1s2s3s4s5 : 6
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,4,3,2,2,2} of size 384
   {2,4,3,2,2,3} of size 576
   {2,4,3,2,2,4} of size 768
   {2,4,3,2,2,5} of size 960
   {2,4,3,2,2,6} of size 1152
   {2,4,3,2,2,7} of size 1344
   {2,4,3,2,2,9} of size 1728
   {2,4,3,2,2,10} of size 1920
Vertex Figure Of :
   {2,2,4,3,2,2} of size 384
   {3,2,4,3,2,2} of size 576
   {4,2,4,3,2,2} of size 768
   {5,2,4,3,2,2} of size 960
   {6,2,4,3,2,2} of size 1152
   {7,2,4,3,2,2} of size 1344
   {9,2,4,3,2,2} of size 1728
   {10,2,4,3,2,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,3,2,4}*384, {2,4,3,2,2}*384, {2,4,6,2,2}*384b, {2,4,6,2,2}*384c
   3-fold covers : {2,4,9,2,2}*576, {2,4,3,2,6}*576, {2,4,3,6,2}*576
   4-fold covers : {4,4,3,2,2}*768a, {2,4,3,2,8}*768, {2,4,12,2,2}*768b, {2,4,12,2,2}*768c, {2,4,3,2,4}*768, {2,4,6,2,4}*768b, {2,4,6,2,4}*768c, {2,4,6,4,2}*768c, {4,4,3,2,2}*768b, {2,8,3,2,2}*768, {2,4,6,2,2}*768, {2,4,3,4,2}*768a
   5-fold covers : {2,4,3,2,10}*960, {2,4,15,2,2}*960
   6-fold covers : {2,4,9,2,4}*1152, {2,4,9,2,2}*1152, {2,4,18,2,2}*1152b, {2,4,18,2,2}*1152c, {2,4,3,2,12}*1152, {2,4,3,6,4}*1152, {2,4,3,2,6}*1152, {2,4,3,6,2}*1152, {2,4,6,2,6}*1152b, {2,4,6,2,6}*1152c, {2,4,6,6,2}*1152d, {2,4,6,6,2}*1152e, {2,4,6,6,2}*1152f, {2,12,3,2,2}*1152, {2,12,6,2,2}*1152d, {6,4,3,2,2}*1152
   7-fold covers : {2,4,3,2,14}*1344, {2,4,21,2,2}*1344
   9-fold covers : {2,4,27,2,2}*1728, {2,4,3,2,18}*1728, {2,4,9,2,6}*1728, {2,4,9,6,2}*1728, {2,4,3,6,2}*1728, {2,4,3,6,6}*1728a, {2,4,3,6,6}*1728b
   10-fold covers : {2,4,3,2,20}*1920, {2,4,15,2,4}*1920, {2,4,3,2,10}*1920, {2,4,6,2,10}*1920b, {2,4,6,2,10}*1920c, {2,4,6,10,2}*1920b, {2,20,6,2,2}*1920b, {10,4,3,2,2}*1920, {2,4,15,2,2}*1920, {2,4,30,2,2}*1920b, {2,4,30,2,2}*1920c
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4)(5,6);;
s2 := (4,5);;
s3 := (5,6);;
s4 := (7,8);;
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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*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, 
s4*s5*s4*s5, s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s1*s2*s3*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(10)!(1,2);
s1 := Sym(10)!(3,4)(5,6);
s2 := Sym(10)!(4,5);
s3 := Sym(10)!(5,6);
s4 := Sym(10)!(7,8);
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*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*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, s4*s5*s4*s5, s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s1*s2*s3*s1*s2 >; 
 

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