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Polytope of Type {2,3,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,6}*96
if this polytope has a name.
Group : SmallGroup(96,226)
Rank : 4
Schlafli Type : {2,3,6}
Number of vertices, edges, etc : 2, 4, 12, 8
Order of s0s1s2s3 : 4
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,3,6,2} of size 192
   {2,3,6,4} of size 384
   {2,3,6,3} of size 480
   {2,3,6,6} of size 576
   {2,3,6,4} of size 768
   {2,3,6,4} of size 768
   {2,3,6,8} of size 768
   {2,3,6,6} of size 960
   {2,3,6,10} of size 960
   {2,3,6,12} of size 1152
   {2,3,6,14} of size 1344
   {2,3,6,4} of size 1440
   {2,3,6,3} of size 1440
   {2,3,6,18} of size 1728
   {2,3,6,20} of size 1920
   {2,3,6,12} of size 1920
Vertex Figure Of :
   {2,2,3,6} of size 192
   {3,2,3,6} of size 288
   {4,2,3,6} of size 384
   {5,2,3,6} of size 480
   {6,2,3,6} of size 576
   {7,2,3,6} of size 672
   {8,2,3,6} of size 768
   {9,2,3,6} of size 864
   {10,2,3,6} of size 960
   {11,2,3,6} of size 1056
   {12,2,3,6} of size 1152
   {13,2,3,6} of size 1248
   {14,2,3,6} of size 1344
   {15,2,3,6} of size 1440
   {17,2,3,6} of size 1632
   {18,2,3,6} of size 1728
   {19,2,3,6} of size 1824
   {20,2,3,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,3,3}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,3,12}*192, {2,6,6}*192
   3-fold covers : {2,3,6}*288
   4-fold covers : {4,3,6}*384b, {2,3,6}*384, {4,6,6}*384, {2,6,12}*384a, {2,12,6}*384a, {2,6,12}*384b, {2,12,6}*384b, {2,6,6}*384b
   5-fold covers : {2,15,6}*480
   6-fold covers : {2,3,12}*576, {6,6,6}*576a, {2,6,6}*576a, {2,6,6}*576b
   7-fold covers : {2,21,6}*672
   8-fold covers : {2,3,12}*768, {4,3,12}*768a, {4,3,6}*768, {4,6,6}*768a, {4,3,12}*768b, {2,12,12}*768a, {4,12,6}*768a, {4,6,12}*768a, {2,6,6}*768c, {2,6,6}*768d, {4,6,6}*768d, {2,6,6}*768e, {2,12,12}*768b, {4,12,6}*768b, {2,6,12}*768, {2,12,6}*768, {2,12,12}*768c, {2,12,12}*768d, {8,6,6}*768, {2,6,24}*768a, {2,24,6}*768a, {4,6,6}*768e, {4,6,12}*768b, {2,6,24}*768b, {2,24,6}*768b
   9-fold covers : {2,9,6}*864, {2,3,6}*864, {6,3,6}*864a
   10-fold covers : {2,15,12}*960, {10,6,6}*960, {2,6,30}*960, {2,30,6}*960
   11-fold covers : {2,33,6}*1056
   12-fold covers : {2,3,6}*1152, {4,3,6}*1152a, {12,6,6}*1152a, {2,6,12}*1152a, {2,12,6}*1152a, {4,6,6}*1152c, {6,6,12}*1152b, {6,12,6}*1152a, {2,6,12}*1152c, {2,12,6}*1152c, {2,6,6}*1152a, {2,6,6}*1152b, {6,6,12}*1152c, {6,12,6}*1152c, {2,6,12}*1152d, {2,12,6}*1152d, {6,6,6}*1152a, {4,6,6}*1152f, {2,6,12}*1152e, {2,12,6}*1152e, {4,3,6}*1152b, {2,3,12}*1152
   13-fold covers : {2,39,6}*1248
   14-fold covers : {2,21,12}*1344, {14,6,6}*1344, {2,6,42}*1344, {2,42,6}*1344
   15-fold covers : {2,15,6}*1440e
   17-fold covers : {2,51,6}*1632
   18-fold covers : {2,9,12}*1728, {2,3,12}*1728, {18,6,6}*1728, {2,6,18}*1728, {2,18,6}*1728, {2,6,6}*1728a, {2,6,6}*1728b, {6,3,12}*1728, {6,6,6}*1728a, {6,6,6}*1728b, {6,6,6}*1728c, {2,6,6}*1728c
   19-fold covers : {2,57,6}*1824
   20-fold covers : {2,15,6}*1920, {4,15,6}*1920, {20,6,6}*1920, {2,6,60}*1920a, {2,60,6}*1920a, {4,30,6}*1920, {10,6,12}*1920a, {10,12,6}*1920a, {2,12,30}*1920a, {2,30,12}*1920a, {2,6,30}*1920, {2,30,6}*1920, {10,6,12}*1920b, {10,12,6}*1920b, {2,6,60}*1920b, {2,60,6}*1920b, {10,6,6}*1920, {4,6,30}*1920, {2,12,30}*1920b, {2,30,12}*1920b
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,6)(4,8);;
s2 := (5,6)(7,8);;
s3 := (3,6)(4,8)(5,7);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(8)!(1,2);
s1 := Sym(8)!(3,6)(4,8);
s2 := Sym(8)!(5,6)(7,8);
s3 := Sym(8)!(3,6)(4,8)(5,7);
poly := sub<Sym(8)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 >; 
 

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