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

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

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