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

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

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