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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,3,2,2}*96
if this polytope has a name.
Group : SmallGroup(96,226)
Rank : 5
Schlafli Type : {4,3,2,2}
Number of vertices, edges, etc : 4, 6, 3, 2, 2
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,3,2,2,2} of size 192
   {4,3,2,2,3} of size 288
   {4,3,2,2,4} of size 384
   {4,3,2,2,5} of size 480
   {4,3,2,2,6} of size 576
   {4,3,2,2,7} of size 672
   {4,3,2,2,8} of size 768
   {4,3,2,2,9} of size 864
   {4,3,2,2,10} of size 960
   {4,3,2,2,11} of size 1056
   {4,3,2,2,12} of size 1152
   {4,3,2,2,13} of size 1248
   {4,3,2,2,14} of size 1344
   {4,3,2,2,15} of size 1440
   {4,3,2,2,17} of size 1632
   {4,3,2,2,18} of size 1728
   {4,3,2,2,19} of size 1824
   {4,3,2,2,20} of size 1920
Vertex Figure Of :
   {2,4,3,2,2} of size 192
   {4,4,3,2,2} of size 768
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,3,2,4}*192, {4,3,2,2}*192, {4,6,2,2}*192b, {4,6,2,2}*192c
   3-fold covers : {4,9,2,2}*288, {4,3,2,6}*288, {4,3,6,2}*288
   4-fold covers : {4,3,2,8}*384, {4,12,2,2}*384b, {4,12,2,2}*384c, {4,3,2,4}*384, {4,6,2,4}*384b, {4,6,2,4}*384c, {4,6,4,2}*384c, {8,3,2,2}*384, {4,6,2,2}*384, {4,3,4,2}*384a
   5-fold covers : {4,3,2,10}*480, {4,15,2,2}*480
   6-fold covers : {4,9,2,4}*576, {4,9,2,2}*576, {4,18,2,2}*576b, {4,18,2,2}*576c, {4,3,2,12}*576, {4,3,6,4}*576, {4,3,2,6}*576, {4,3,6,2}*576, {4,6,2,6}*576b, {4,6,2,6}*576c, {4,6,6,2}*576d, {4,6,6,2}*576e, {4,6,6,2}*576f, {12,3,2,2}*576, {12,6,2,2}*576d
   7-fold covers : {4,3,2,14}*672, {4,21,2,2}*672
   8-fold covers : {4,3,2,16}*768, {4,12,4,2}*768d, {4,12,4,2}*768e, {4,6,4,4}*768b, {4,12,2,4}*768b, {4,12,2,4}*768c, {8,3,2,2}*768, {8,6,2,2}*768a, {4,6,2,2}*768a, {4,24,2,2}*768c, {4,24,2,2}*768d, {4,3,2,8}*768, {4,6,2,8}*768b, {4,6,2,8}*768c, {4,6,8,2}*768b, {8,3,2,4}*768, {4,12,2,2}*768b, {4,6,2,2}*768b, {4,6,2,4}*768, {4,6,4,2}*768b, {4,12,2,2}*768c, {8,6,2,2}*768b, {8,6,2,2}*768c, {4,3,4,4}*768b, {4,3,8,2}*768, {4,3,4,2}*768, {4,6,4,2}*768c, {4,6,4,2}*768f
   9-fold covers : {4,27,2,2}*864, {4,3,2,18}*864, {4,9,2,6}*864, {4,9,6,2}*864, {4,3,6,6}*864a, {4,3,6,2}*864, {4,3,6,6}*864b
   10-fold covers : {4,3,2,20}*960, {4,15,2,4}*960, {4,3,2,10}*960, {4,6,2,10}*960b, {4,6,2,10}*960c, {4,6,10,2}*960b, {20,6,2,2}*960b, {4,15,2,2}*960, {4,30,2,2}*960b, {4,30,2,2}*960c
   11-fold covers : {4,3,2,22}*1056, {4,33,2,2}*1056
   12-fold covers : {4,9,2,8}*1152, {4,36,2,2}*1152b, {4,36,2,2}*1152c, {4,9,2,4}*1152, {4,18,2,4}*1152b, {4,18,2,4}*1152c, {4,18,4,2}*1152c, {8,9,2,2}*1152, {4,3,2,24}*1152, {4,3,6,8}*1152, {4,18,2,2}*1152, {4,9,4,2}*1152a, {4,12,2,6}*1152b, {4,12,2,6}*1152c, {4,12,6,2}*1152d, {4,12,6,2}*1152e, {4,12,6,2}*1152f, {4,12,6,2}*1152g, {4,3,2,12}*1152, {4,6,2,12}*1152b, {4,6,2,12}*1152c, {4,6,12,2}*1152d, {4,6,4,6}*1152b, {4,6,6,4}*1152e, {12,3,2,4}*1152, {12,6,2,4}*1152d, {24,3,2,2}*1152, {8,3,2,6}*1152, {8,3,6,2}*1152, {4,3,6,4}*1152, {4,6,6,4}*1152f, {4,6,6,4}*1152i, {4,6,12,2}*1152e, {4,3,6,2}*1152, {4,6,2,6}*1152, {4,6,6,2}*1152a, {4,6,6,2}*1152b, {12,6,2,2}*1152a, {12,6,2,2}*1152b, {4,3,4,6}*1152, {4,3,12,2}*1152
   13-fold covers : {4,3,2,26}*1248, {4,39,2,2}*1248
   14-fold covers : {4,3,2,28}*1344, {4,21,2,4}*1344, {4,3,2,14}*1344, {4,6,2,14}*1344b, {4,6,2,14}*1344c, {4,6,14,2}*1344b, {28,6,2,2}*1344b, {4,21,2,2}*1344, {4,42,2,2}*1344b, {4,42,2,2}*1344c
   15-fold covers : {4,9,2,10}*1440, {4,45,2,2}*1440, {4,3,6,10}*1440, {4,15,2,6}*1440, {4,15,6,2}*1440, {4,3,2,30}*1440
   17-fold covers : {4,3,2,34}*1632, {4,51,2,2}*1632
   18-fold covers : {4,27,2,4}*1728, {4,27,2,2}*1728, {4,54,2,2}*1728b, {4,54,2,2}*1728c, {4,3,2,36}*1728, {4,9,2,12}*1728, {4,3,6,12}*1728a, {4,9,6,4}*1728, {4,3,6,4}*1728a, {4,3,2,18}*1728, {4,6,2,18}*1728b, {4,6,2,18}*1728c, {4,6,18,2}*1728c, {36,6,2,2}*1728c, {4,9,2,6}*1728, {4,9,6,2}*1728, {4,18,2,6}*1728b, {4,18,2,6}*1728c, {4,18,6,2}*1728c, {4,18,6,2}*1728d, {4,18,6,2}*1728e, {12,9,2,2}*1728, {12,18,2,2}*1728c, {4,3,6,6}*1728a, {4,6,6,6}*1728b, {4,6,6,6}*1728c, {4,3,6,2}*1728, {4,6,6,2}*1728d, {4,6,6,2}*1728e, {4,6,6,2}*1728f, {12,3,2,2}*1728, {12,6,2,2}*1728d, {4,3,6,12}*1728b, {4,3,6,4}*1728b, {4,3,6,6}*1728b, {4,6,6,6}*1728j, {4,6,6,6}*1728k, {4,6,6,6}*1728l, {4,6,6,6}*1728m, {4,6,6,6}*1728n, {4,6,6,2}*1728i, {12,3,2,6}*1728, {12,3,6,2}*1728, {12,6,2,6}*1728d, {12,6,6,2}*1728h
   19-fold covers : {4,3,2,38}*1824, {4,57,2,2}*1824
   20-fold covers : {4,3,2,40}*1920, {4,15,2,8}*1920, {4,12,2,10}*1920b, {4,12,2,10}*1920c, {4,12,10,2}*1920b, {4,12,10,2}*1920c, {4,3,2,20}*1920, {4,6,2,20}*1920b, {4,6,2,20}*1920c, {4,6,20,2}*1920b, {4,6,4,10}*1920b, {4,6,10,4}*1920b, {20,6,2,4}*1920b, {8,3,2,10}*1920, {4,60,2,2}*1920b, {4,60,2,2}*1920c, {4,15,2,4}*1920, {4,30,2,4}*1920b, {4,30,2,4}*1920c, {4,30,4,2}*1920c, {8,15,2,2}*1920, {4,6,2,10}*1920, {4,6,10,2}*1920a, {20,6,2,2}*1920a, {4,3,4,10}*1920, {4,30,2,2}*1920, {4,15,4,2}*1920a
Permutation Representation (GAP) :
s0 := (1,2)(3,4);;
s1 := (2,3);;
s2 := (3,4);;
s3 := (5,6);;
s4 := (7,8);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(8)!(1,2)(3,4);
s1 := Sym(8)!(2,3);
s2 := Sym(8)!(3,4);
s3 := Sym(8)!(5,6);
s4 := Sym(8)!(7,8);
poly := sub<Sym(8)|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*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1 >; 
 

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