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Polytope of Type {4,3,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,3,2}*96
if this polytope has a name.
Group : SmallGroup(96,226)
Rank : 4
Schlafli Type : {4,3,2}
Number of vertices, edges, etc : 8, 12, 6, 2
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Locally Projective
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,3,2,2} of size 192
   {4,3,2,3} of size 288
   {4,3,2,4} of size 384
   {4,3,2,5} of size 480
   {4,3,2,6} of size 576
   {4,3,2,7} of size 672
   {4,3,2,8} of size 768
   {4,3,2,9} of size 864
   {4,3,2,10} of size 960
   {4,3,2,11} of size 1056
   {4,3,2,12} of size 1152
   {4,3,2,13} of size 1248
   {4,3,2,14} of size 1344
   {4,3,2,15} of size 1440
   {4,3,2,17} of size 1632
   {4,3,2,18} of size 1728
   {4,3,2,19} of size 1824
   {4,3,2,20} of size 1920
Vertex Figure Of :
   {2,4,3,2} of size 192
   {4,4,3,2} of size 384
   {6,4,3,2} of size 576
   {4,4,3,2} of size 768
   {8,4,3,2} of size 768
   {10,4,3,2} of size 960
   {12,4,3,2} of size 1152
   {3,4,3,2} of size 1152
   {14,4,3,2} of size 1344
   {4,4,3,2} of size 1440
   {18,4,3,2} of size 1728
   {20,4,3,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,3,2}*48
   4-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,3,2}*192, {4,6,2}*192
   3-fold covers : {4,9,2}*288, {4,3,6}*288, {12,3,2}*288
   4-fold covers : {8,3,2}*384, {4,12,2}*384b, {4,6,4}*384b, {4,6,2}*384b, {4,12,2}*384c, {8,6,2}*384b, {8,6,2}*384c, {4,3,4}*384
   5-fold covers : {4,15,2}*480
   6-fold covers : {8,9,2}*576, {4,18,2}*576, {24,3,2}*576, {8,3,6}*576, {4,6,6}*576a, {4,6,6}*576b, {12,6,2}*576a, {12,6,2}*576b
   7-fold covers : {4,21,2}*672
   8-fold covers : {8,3,2}*768, {8,6,2}*768a, {4,12,4}*768f, {4,12,2}*768d, {4,6,4}*768d, {4,12,4}*768h, {8,6,2}*768d, {8,6,2}*768e, {4,6,2}*768a, {8,12,2}*768e, {8,12,2}*768f, {4,24,2}*768c, {4,24,2}*768d, {8,6,2}*768f, {8,12,2}*768g, {8,12,2}*768h, {4,6,8}*768a, {8,6,2}*768g, {8,6,4}*768b, {8,6,4}*768c, {4,6,2}*768b, {4,24,2}*768e, {4,12,2}*768e, {4,24,2}*768f, {4,3,8}*768b, {8,3,4}*768b, {4,3,8}*768c, {8,3,4}*768c, {4,3,4}*768, {4,6,4}*768j, {4,6,4}*768l
   9-fold covers : {4,27,2}*864, {4,9,6}*864, {12,9,2}*864, {4,3,6}*864, {12,3,2}*864, {12,3,6}*864
   10-fold covers : {8,15,2}*960, {4,6,10}*960e, {20,6,2}*960c, {4,30,2}*960
   11-fold covers : {4,33,2}*1056
   12-fold covers : {8,9,2}*1152, {4,36,2}*1152b, {4,18,4}*1152b, {4,18,2}*1152b, {4,36,2}*1152c, {8,18,2}*1152b, {8,18,2}*1152c, {24,3,2}*1152, {8,3,6}*1152, {4,9,4}*1152, {4,12,6}*1152e, {4,12,6}*1152f, {12,12,2}*1152f, {12,12,2}*1152g, {4,6,12}*1152a, {12,6,2}*1152b, {12,12,2}*1152i, {4,6,6}*1152d, {4,6,6}*1152e, {4,12,6}*1152h, {4,12,6}*1152i, {12,6,4}*1152b, {12,6,4}*1152c, {24,6,2}*1152b, {24,6,2}*1152c, {24,6,2}*1152d, {8,6,6}*1152b, {8,6,6}*1152c, {24,6,2}*1152e, {8,6,6}*1152d, {8,6,6}*1152e, {4,6,12}*1152d, {12,6,2}*1152f, {12,12,2}*1152k, {4,3,6}*1152b, {12,3,2}*1152, {4,3,12}*1152b, {12,3,4}*1152b
   13-fold covers : {4,39,2}*1248
   14-fold covers : {8,21,2}*1344, {4,6,14}*1344, {28,6,2}*1344, {4,42,2}*1344
   15-fold covers : {4,45,2}*1440, {4,15,6}*1440b, {12,15,2}*1440
   17-fold covers : {4,51,2}*1632
   18-fold covers : {8,27,2}*1728, {4,54,2}*1728, {24,9,2}*1728, {24,3,2}*1728, {8,9,6}*1728, {8,3,6}*1728, {4,6,18}*1728, {36,6,2}*1728, {4,18,6}*1728a, {4,18,6}*1728b, {12,18,2}*1728a, {12,18,2}*1728b, {4,6,6}*1728a, {4,6,6}*1728b, {12,6,2}*1728a, {12,6,2}*1728b, {24,3,6}*1728, {4,6,6}*1728c, {12,6,6}*1728a, {12,6,6}*1728b, {12,6,6}*1728c, {12,6,6}*1728d, {12,6,2}*1728c
   19-fold covers : {4,57,2}*1824
   20-fold covers : {8,15,2}*1920a, {4,12,10}*1920b, {20,12,2}*1920b, {4,6,20}*1920a, {20,6,2}*1920a, {4,6,10}*1920b, {4,12,10}*1920c, {20,6,4}*1920b, {40,6,2}*1920b, {8,6,10}*1920a, {40,6,2}*1920c, {8,6,10}*1920b, {20,12,2}*1920c, {4,60,2}*1920b, {4,30,4}*1920b, {4,30,2}*1920b, {4,60,2}*1920c, {8,30,2}*1920b, {8,30,2}*1920c, {4,15,4}*1920c
Permutation Representation (GAP) :
s0 := (4,6);;
s1 := (3,4)(5,6);;
s2 := (1,3)(2,5);;
s3 := (7,8);;
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, s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(8)!(4,6);
s1 := Sym(8)!(3,4)(5,6);
s2 := Sym(8)!(1,3)(2,5);
s3 := Sym(8)!(7,8);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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