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Polytope of Type {2,2,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,6,4}*192a
if this polytope has a name.
Group : SmallGroup(192,1514)
Rank : 5
Schlafli Type : {2,2,6,4}
Number of vertices, edges, etc : 2, 2, 6, 12, 4
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,6,4,2} of size 384
   {2,2,6,4,4} of size 768
   {2,2,6,4,6} of size 1152
   {2,2,6,4,3} of size 1152
   {2,2,6,4,6} of size 1728
   {2,2,6,4,10} of size 1920
Vertex Figure Of :
   {2,2,2,6,4} of size 384
   {3,2,2,6,4} of size 576
   {4,2,2,6,4} of size 768
   {5,2,2,6,4} of size 960
   {6,2,2,6,4} of size 1152
   {7,2,2,6,4} of size 1344
   {9,2,2,6,4} of size 1728
   {10,2,2,6,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,6,2}*96
   3-fold quotients : {2,2,2,4}*64
   4-fold quotients : {2,2,3,2}*48
   6-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,2,12,4}*384a, {2,4,6,4}*384a, {4,2,6,4}*384a, {2,2,6,8}*384
   3-fold covers : {2,2,18,4}*576a, {2,2,6,12}*576a, {2,6,6,4}*576a, {2,6,6,4}*576b, {6,2,6,4}*576a, {2,2,6,12}*576c
   4-fold covers : {2,4,12,4}*768a, {4,4,6,4}*768a, {4,2,12,4}*768a, {2,2,12,8}*768a, {2,2,24,4}*768a, {2,2,12,8}*768b, {2,2,24,4}*768b, {2,2,12,4}*768a, {4,2,6,8}*768, {8,2,6,4}*768a, {2,4,6,8}*768a, {2,8,6,4}*768a, {2,2,6,16}*768, {2,2,6,4}*768b, {2,4,6,4}*768b
   5-fold covers : {2,2,6,20}*960a, {2,10,6,4}*960a, {10,2,6,4}*960a, {2,2,30,4}*960a
   6-fold covers : {2,2,36,4}*1152a, {2,6,12,4}*1152a, {2,6,12,4}*1152b, {6,2,12,4}*1152a, {2,2,12,12}*1152a, {2,2,12,12}*1152c, {4,2,18,4}*1152a, {2,4,18,4}*1152a, {6,4,6,4}*1152a, {4,6,6,4}*1152a, {4,6,6,4}*1152c, {4,2,6,12}*1152a, {4,2,6,12}*1152b, {12,2,6,4}*1152a, {2,4,6,12}*1152a, {2,12,6,4}*1152a, {2,4,6,12}*1152b, {2,12,6,4}*1152b, {2,2,18,8}*1152, {2,6,6,8}*1152a, {2,6,6,8}*1152b, {6,2,6,8}*1152, {2,2,6,24}*1152a, {2,2,6,24}*1152b
   7-fold covers : {2,2,6,28}*1344a, {2,14,6,4}*1344a, {14,2,6,4}*1344a, {2,2,42,4}*1344a
   9-fold covers : {2,2,54,4}*1728a, {2,2,18,12}*1728a, {2,2,6,36}*1728a, {2,2,6,12}*1728b, {2,6,18,4}*1728a, {2,6,18,4}*1728b, {2,18,6,4}*1728a, {6,2,18,4}*1728a, {18,2,6,4}*1728a, {6,6,6,4}*1728a, {2,6,6,4}*1728a, {2,6,6,4}*1728b, {2,2,18,12}*1728b, {2,2,6,12}*1728c, {2,6,6,12}*1728b, {2,6,6,12}*1728d, {6,2,6,12}*1728a, {6,6,6,4}*1728d, {6,6,6,4}*1728e, {6,6,6,4}*1728f, {2,2,6,12}*1728g, {2,6,6,4}*1728h, {2,6,6,12}*1728f, {2,6,6,12}*1728g, {6,2,6,12}*1728c, {6,6,6,4}*1728i, {2,2,6,4}*1728b
   10-fold covers : {2,2,60,4}*1920a, {2,10,12,4}*1920a, {10,2,12,4}*1920a, {2,2,12,20}*1920, {4,2,30,4}*1920a, {2,4,30,4}*1920a, {10,4,6,4}*1920a, {4,10,6,4}*1920a, {4,2,6,20}*1920a, {20,2,6,4}*1920a, {2,4,6,20}*1920a, {2,20,6,4}*1920a, {2,2,30,8}*1920, {2,10,6,8}*1920, {10,2,6,8}*1920, {2,2,6,40}*1920
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 7, 8)(10,11)(13,14)(15,16);;
s3 := ( 5, 7)( 6,13)( 9,10)(11,14)(12,15);;
s4 := ( 5, 6)( 7,10)( 8,11)( 9,12)(13,15)(14,16);;
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*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(16)!(1,2);
s1 := Sym(16)!(3,4);
s2 := Sym(16)!( 7, 8)(10,11)(13,14)(15,16);
s3 := Sym(16)!( 5, 7)( 6,13)( 9,10)(11,14)(12,15);
s4 := Sym(16)!( 5, 6)( 7,10)( 8,11)( 9,12)(13,15)(14,16);
poly := sub<Sym(16)|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*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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