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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,2,2,3}*192
if this polytope has a name.
Group : SmallGroup(192,1514)
Rank : 6
Schlafli Type : {4,2,2,2,3}
Number of vertices, edges, etc : 4, 4, 2, 2, 3, 3
Order of s0s1s2s3s4s5 : 12
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,2,2,2,3,2} of size 384
   {4,2,2,2,3,3} of size 768
   {4,2,2,2,3,4} of size 768
   {4,2,2,2,3,6} of size 1152
   {4,2,2,2,3,5} of size 1920
Vertex Figure Of :
   {2,4,2,2,2,3} of size 384
   {3,4,2,2,2,3} of size 576
   {4,4,2,2,2,3} of size 768
   {6,4,2,2,2,3} of size 1152
   {3,4,2,2,2,3} of size 1152
   {6,4,2,2,2,3} of size 1152
   {6,4,2,2,2,3} of size 1152
   {9,4,2,2,2,3} of size 1728
   {4,4,2,2,2,3} of size 1728
   {6,4,2,2,2,3} of size 1728
   {10,4,2,2,2,3} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,2,2,3}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,4,2,2,3}*384, {4,2,4,2,3}*384, {8,2,2,2,3}*384, {4,2,2,2,6}*384
   3-fold covers : {4,2,2,2,9}*576, {12,2,2,2,3}*576, {4,2,2,6,3}*576, {4,2,6,2,3}*576, {4,6,2,2,3}*576a
   4-fold covers : {4,4,4,2,3}*768, {4,8,2,2,3}*768a, {8,4,2,2,3}*768a, {4,8,2,2,3}*768b, {8,4,2,2,3}*768b, {4,4,2,2,3}*768, {4,2,8,2,3}*768, {8,2,4,2,3}*768, {16,2,2,2,3}*768, {4,4,2,2,6}*768, {4,2,2,4,6}*768a, {4,2,4,2,6}*768, {4,2,2,2,12}*768, {8,2,2,2,6}*768, {4,2,2,4,3}*768
   5-fold covers : {20,2,2,2,3}*960, {4,2,10,2,3}*960, {4,10,2,2,3}*960, {4,2,2,2,15}*960
   6-fold covers : {4,4,2,2,9}*1152, {4,4,2,6,3}*1152, {4,4,6,2,3}*1152, {4,12,2,2,3}*1152a, {12,4,2,2,3}*1152a, {4,2,4,2,9}*1152, {4,6,4,2,3}*1152a, {4,2,4,6,3}*1152, {4,2,12,2,3}*1152, {12,2,4,2,3}*1152, {8,2,2,2,9}*1152, {8,2,2,6,3}*1152, {8,2,6,2,3}*1152, {8,6,2,2,3}*1152, {24,2,2,2,3}*1152, {4,2,2,2,18}*1152, {4,2,2,6,6}*1152a, {4,2,2,6,6}*1152b, {4,2,6,2,6}*1152, {4,6,2,2,6}*1152a, {12,2,2,2,6}*1152
   7-fold covers : {28,2,2,2,3}*1344, {4,2,14,2,3}*1344, {4,14,2,2,3}*1344, {4,2,2,2,21}*1344
   9-fold covers : {4,2,2,2,27}*1728, {12,2,2,2,9}*1728, {36,2,2,2,3}*1728, {4,2,2,6,9}*1728, {4,2,6,2,9}*1728, {4,2,18,2,3}*1728, {4,6,2,2,9}*1728a, {4,18,2,2,3}*1728a, {4,2,2,6,3}*1728, {4,2,6,6,3}*1728a, {12,2,2,6,3}*1728, {12,2,6,2,3}*1728, {12,6,2,2,3}*1728a, {12,6,2,2,3}*1728b, {4,2,6,6,3}*1728b, {4,6,2,6,3}*1728a, {4,6,6,2,3}*1728a, {4,6,6,2,3}*1728b, {4,6,6,2,3}*1728c, {12,6,2,2,3}*1728c, {4,6,2,2,3}*1728
   10-fold covers : {4,4,2,2,15}*1920, {4,4,10,2,3}*1920, {4,20,2,2,3}*1920, {20,4,2,2,3}*1920, {4,2,4,2,15}*1920, {4,10,4,2,3}*1920, {4,2,20,2,3}*1920, {20,2,4,2,3}*1920, {8,2,2,2,15}*1920, {8,2,10,2,3}*1920, {8,10,2,2,3}*1920, {40,2,2,2,3}*1920, {4,2,2,2,30}*1920, {4,2,2,10,6}*1920, {4,2,10,2,6}*1920, {4,10,2,2,6}*1920, {20,2,2,2,6}*1920
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := (5,6);;
s3 := (7,8);;
s4 := (10,11);;
s5 := ( 9,10);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s2*s0*s2, s1*s2*s1*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, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5*s4*s5, s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(11)!(2,3);
s1 := Sym(11)!(1,2)(3,4);
s2 := Sym(11)!(5,6);
s3 := Sym(11)!(7,8);
s4 := Sym(11)!(10,11);
s5 := Sym(11)!( 9,10);
poly := sub<Sym(11)|s0,s1,s2,s3,s4,s5>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s2*s0*s2, s1*s2*s1*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, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5*s4*s5, 
s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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