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Polytope of Type {6,4,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4,2}*192
if this polytope has a name.
Group : SmallGroup(192,1537)
Rank : 4
Schlafli Type : {6,4,2}
Number of vertices, edges, etc : 12, 24, 8, 2
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,4,2,2} of size 384
   {6,4,2,3} of size 576
   {6,4,2,4} of size 768
   {6,4,2,5} of size 960
   {6,4,2,6} of size 1152
   {6,4,2,7} of size 1344
   {6,4,2,9} of size 1728
   {6,4,2,10} of size 1920
Vertex Figure Of :
   {2,6,4,2} of size 384
   {3,6,4,2} of size 768
   {3,6,4,2} of size 768
   {4,6,4,2} of size 768
   {4,6,4,2} of size 768
   {4,6,4,2} of size 768
   {6,6,4,2} of size 1152
   {6,6,4,2} of size 1152
   {6,6,4,2} of size 1728
   {10,6,4,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,4,2}*96, {6,4,2}*96b, {6,4,2}*96c
   4-fold quotients : {3,4,2}*48, {6,2,2}*48
   8-fold quotients : {3,2,2}*24
   12-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,4,2}*384b, {6,4,4}*384d, {6,4,2}*384b, {12,4,2}*384c, {6,8,2}*384b, {6,8,2}*384c
   3-fold covers : {18,4,2}*576, {6,4,6}*576b, {6,12,2}*576a, {6,12,2}*576b
   4-fold covers : {12,4,2}*768d, {6,4,4}*768e, {12,4,4}*768e, {12,4,4}*768f, {6,8,2}*768d, {6,8,2}*768e, {6,4,4}*768f, {6,4,2}*768a, {12,8,2}*768e, {12,8,2}*768f, {24,4,2}*768c, {24,4,2}*768d, {6,8,4}*768c, {6,8,2}*768f, {12,8,2}*768g, {12,8,2}*768h, {6,4,8}*768c, {6,8,2}*768g, {6,8,4}*768d, {6,4,2}*768b, {24,4,2}*768e, {12,4,2}*768e, {24,4,2}*768f
   5-fold covers : {6,4,10}*960, {6,20,2}*960c, {30,4,2}*960
   6-fold covers : {36,4,2}*1152b, {18,4,4}*1152d, {18,4,2}*1152b, {36,4,2}*1152c, {18,8,2}*1152b, {18,8,2}*1152c, {12,4,6}*1152b, {12,12,2}*1152d, {12,12,2}*1152e, {6,4,12}*1152c, {6,12,2}*1152b, {12,12,2}*1152h, {6,4,6}*1152b, {6,12,4}*1152i, {12,4,6}*1152d, {6,24,2}*1152b, {6,24,2}*1152c, {6,24,2}*1152d, {6,8,6}*1152b, {6,24,2}*1152e, {6,8,6}*1152d, {6,12,4}*1152j, {6,12,2}*1152f, {12,12,2}*1152j
   7-fold covers : {6,4,14}*1344, {6,28,2}*1344, {42,4,2}*1344
   9-fold covers : {54,4,2}*1728, {6,4,18}*1728a, {6,36,2}*1728, {18,4,6}*1728b, {18,12,2}*1728a, {18,12,2}*1728b, {6,12,6}*1728b, {6,12,2}*1728a, {6,12,2}*1728b, {6,12,6}*1728i, {6,12,6}*1728j, {6,12,6}*1728k, {6,12,6}*1728l, {6,12,2}*1728c
   10-fold covers : {12,4,10}*1920b, {12,20,2}*1920b, {6,4,20}*1920b, {6,20,2}*1920a, {6,4,10}*1920, {6,20,4}*1920c, {12,4,10}*1920c, {6,40,2}*1920b, {6,8,10}*1920a, {6,40,2}*1920c, {6,8,10}*1920b, {12,20,2}*1920c, {60,4,2}*1920b, {30,4,4}*1920d, {30,4,2}*1920b, {60,4,2}*1920c, {30,8,2}*1920b, {30,8,2}*1920c
Permutation Representation (GAP) :
s0 := ( 8, 9)(11,12)(13,14)(15,16);;
s1 := ( 1, 2)( 3, 5)( 4,11)( 6, 8)( 7,15)( 9,12)(10,13)(14,16);;
s2 := ( 1, 7)( 2,10)( 3, 4)( 5, 6)( 8,14)( 9,13)(11,16)(12,15);;
s3 := (17,18);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(18)!( 8, 9)(11,12)(13,14)(15,16);
s1 := Sym(18)!( 1, 2)( 3, 5)( 4,11)( 6, 8)( 7,15)( 9,12)(10,13)(14,16);
s2 := Sym(18)!( 1, 7)( 2,10)( 3, 4)( 5, 6)( 8,14)( 9,13)(11,16)(12,15);
s3 := Sym(18)!(17,18);
poly := sub<Sym(18)|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, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1 >; 
 

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