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Polytope of Type {2,2,4,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,6}*192c
if this polytope has a name.
Group : SmallGroup(192,1537)
Rank : 5
Schlafli Type : {2,2,4,6}
Number of vertices, edges, etc : 2, 2, 4, 12, 6
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,4,6,2} of size 384
   {2,2,4,6,4} of size 768
   {2,2,4,6,4} of size 768
   {2,2,4,6,4} of size 768
   {2,2,4,6,6} of size 1152
   {2,2,4,6,6} of size 1152
   {2,2,4,6,6} of size 1728
   {2,2,4,6,10} of size 1920
Vertex Figure Of :
   {2,2,2,4,6} of size 384
   {3,2,2,4,6} of size 576
   {4,2,2,4,6} of size 768
   {5,2,2,4,6} of size 960
   {6,2,2,4,6} of size 1152
   {7,2,2,4,6} of size 1344
   {9,2,2,4,6} of size 1728
   {10,2,2,4,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,4,3}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,2,4,12}*384b, {2,2,4,12}*384c, {4,2,4,6}*384c, {2,2,4,6}*384
   3-fold covers : {2,2,4,18}*576b, {6,2,4,6}*576c
   4-fold covers : {4,2,4,12}*768b, {4,2,4,12}*768c, {2,2,4,6}*768a, {2,4,4,6}*768b, {2,2,4,24}*768c, {2,2,4,24}*768d, {8,2,4,6}*768c, {2,2,4,12}*768b, {2,2,4,6}*768b, {2,2,4,12}*768c, {2,4,4,6}*768d, {4,2,4,6}*768, {2,2,8,6}*768b, {2,2,8,6}*768c
   5-fold covers : {10,2,4,6}*960c, {2,2,4,30}*960b
   6-fold covers : {2,2,4,36}*1152b, {2,2,4,36}*1152c, {4,2,4,18}*1152b, {2,2,4,18}*1152, {6,2,4,12}*1152b, {6,2,4,12}*1152c, {12,2,4,6}*1152c, {2,2,12,6}*1152a, {2,2,12,6}*1152b, {2,6,4,6}*1152a, {6,2,4,6}*1152
   7-fold covers : {14,2,4,6}*1344c, {2,2,4,42}*1344b
   9-fold covers : {2,2,4,54}*1728b, {18,2,4,6}*1728c, {6,2,4,18}*1728b
   10-fold covers : {10,2,4,12}*1920b, {10,2,4,12}*1920c, {20,2,4,6}*1920c, {2,2,4,60}*1920b, {2,2,4,60}*1920c, {4,2,4,30}*1920b, {2,2,20,6}*1920a, {2,10,4,6}*1920, {10,2,4,6}*1920, {2,2,4,30}*1920
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 7, 9)( 8,10);;
s3 := (5,7)(6,9);;
s4 := ( 5, 6)( 7, 8)( 9,10);;
poly := Group([s0,s1,s2,s3,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(10)!(1,2);
s1 := Sym(10)!(3,4);
s2 := Sym(10)!( 7, 9)( 8,10);
s3 := Sym(10)!(5,7)(6,9);
s4 := Sym(10)!( 5, 6)( 7, 8)( 9,10);
poly := sub<Sym(10)|s0,s1,s2,s3,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

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