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

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

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