Polytope of Type {2,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,4}*96a
if this polytope has a name.
Group : SmallGroup(96,209)
Rank : 4
Schlafli Type : {2,6,4}
Number of vertices, edges, etc : 2, 6, 12, 4
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,4,2} of size 192
   {2,6,4,4} of size 384
   {2,6,4,6} of size 576
   {2,6,4,3} of size 576
   {2,6,4,8} of size 768
   {2,6,4,8} of size 768
   {2,6,4,4} of size 768
   {2,6,4,6} of size 864
   {2,6,4,10} of size 960
   {2,6,4,12} of size 1152
   {2,6,4,6} of size 1152
   {2,6,4,14} of size 1344
   {2,6,4,5} of size 1440
   {2,6,4,18} of size 1728
   {2,6,4,9} of size 1728
   {2,6,4,4} of size 1728
   {2,6,4,6} of size 1728
   {2,6,4,20} of size 1920
Vertex Figure Of :
   {2,2,6,4} of size 192
   {3,2,6,4} of size 288
   {4,2,6,4} of size 384
   {5,2,6,4} of size 480
   {6,2,6,4} of size 576
   {7,2,6,4} of size 672
   {8,2,6,4} of size 768
   {9,2,6,4} of size 864
   {10,2,6,4} of size 960
   {11,2,6,4} of size 1056
   {12,2,6,4} of size 1152
   {13,2,6,4} of size 1248
   {14,2,6,4} of size 1344
   {15,2,6,4} of size 1440
   {17,2,6,4} of size 1632
   {18,2,6,4} of size 1728
   {19,2,6,4} of size 1824
   {20,2,6,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,6,2}*48
   3-fold quotients : {2,2,4}*32
   4-fold quotients : {2,3,2}*24
   6-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,12,4}*192a, {4,6,4}*192a, {2,6,8}*192
   3-fold covers : {2,18,4}*288a, {2,6,12}*288a, {6,6,4}*288a, {6,6,4}*288b, {2,6,12}*288c
   4-fold covers : {4,12,4}*384a, {2,24,4}*384a, {2,12,4}*384a, {2,24,4}*384b, {2,12,8}*384a, {2,12,8}*384b, {4,6,8}*384a, {8,6,4}*384a, {2,6,16}*384, {4,6,4}*384b, {2,6,4}*384b
   5-fold covers : {2,6,20}*480a, {10,6,4}*480a, {2,30,4}*480a
   6-fold covers : {2,36,4}*576a, {4,18,4}*576a, {2,18,8}*576, {6,12,4}*576a, {6,12,4}*576b, {4,6,12}*576a, {12,6,4}*576a, {2,6,24}*576a, {6,6,8}*576a, {6,6,8}*576b, {2,12,12}*576a, {2,12,12}*576c, {2,6,24}*576c, {4,6,12}*576c, {12,6,4}*576c
   7-fold covers : {2,6,28}*672a, {14,6,4}*672a, {2,42,4}*672a
   8-fold covers : {2,12,8}*768a, {2,24,4}*768a, {2,24,8}*768a, {2,24,8}*768b, {2,24,8}*768c, {2,24,8}*768d, {8,6,8}*768, {4,12,8}*768a, {8,12,4}*768a, {4,12,8}*768b, {8,12,4}*768b, {4,24,4}*768a, {4,12,4}*768a, {4,12,4}*768b, {4,24,4}*768b, {4,24,4}*768c, {4,24,4}*768d, {2,12,16}*768a, {2,48,4}*768a, {2,12,16}*768b, {2,48,4}*768b, {2,12,4}*768a, {2,24,4}*768b, {2,12,8}*768b, {4,6,16}*768a, {16,6,4}*768a, {2,6,32}*768, {4,12,4}*768f, {2,12,4}*768d, {4,6,4}*768c, {4,6,4}*768d, {4,12,4}*768h, {2,6,8}*768f, {4,6,8}*768a, {2,6,8}*768g, {8,6,4}*768b, {8,6,4}*768c, {2,6,4}*768b, {2,12,4}*768e
   9-fold covers : {2,54,4}*864a, {2,6,36}*864a, {2,18,12}*864a, {2,6,12}*864b, {6,18,4}*864a, {6,18,4}*864b, {18,6,4}*864a, {6,6,4}*864a, {6,6,4}*864b, {2,18,12}*864b, {2,6,12}*864c, {6,6,12}*864b, {6,6,12}*864d, {2,6,12}*864g, {6,6,4}*864h, {6,6,12}*864f, {6,6,12}*864g, {2,6,4}*864b
   10-fold covers : {10,12,4}*960a, {4,6,20}*960a, {20,6,4}*960a, {2,6,40}*960, {10,6,8}*960, {2,12,20}*960, {2,60,4}*960a, {4,30,4}*960a, {2,30,8}*960
   11-fold covers : {2,6,44}*1056a, {22,6,4}*1056a, {2,66,4}*1056a
   12-fold covers : {4,36,4}*1152a, {4,12,12}*1152a, {4,12,12}*1152b, {12,12,4}*1152a, {12,12,4}*1152b, {2,36,8}*1152a, {2,72,4}*1152a, {6,12,8}*1152a, {6,12,8}*1152b, {6,24,4}*1152b, {6,24,4}*1152c, {2,12,24}*1152a, {2,24,12}*1152a, {2,24,12}*1152b, {2,12,24}*1152c, {2,36,8}*1152b, {2,72,4}*1152b, {6,12,8}*1152d, {6,12,8}*1152e, {6,24,4}*1152e, {6,24,4}*1152f, {2,12,24}*1152d, {2,24,12}*1152d, {2,24,12}*1152e, {2,12,24}*1152f, {2,36,4}*1152a, {6,12,4}*1152a, {6,12,4}*1152b, {2,12,12}*1152a, {2,12,12}*1152c, {4,18,8}*1152a, {8,18,4}*1152a, {8,6,12}*1152a, {12,6,8}*1152a, {8,6,12}*1152b, {12,6,8}*1152b, {4,6,24}*1152a, {24,6,4}*1152a, {4,6,24}*1152b, {24,6,4}*1152b, {2,18,16}*1152, {6,6,16}*1152a, {6,6,16}*1152b, {2,6,48}*1152a, {2,6,48}*1152b, {4,18,4}*1152b, {2,18,4}*1152b, {2,12,12}*1152f, {4,6,12}*1152a, {2,6,12}*1152b, {6,6,4}*1152c, {6,6,4}*1152d, {6,6,4}*1152e, {6,12,4}*1152i, {12,6,4}*1152b, {12,6,4}*1152c, {4,6,12}*1152d, {2,6,12}*1152e, {2,6,12}*1152f
   13-fold covers : {2,6,52}*1248a, {26,6,4}*1248a, {2,78,4}*1248a
   14-fold covers : {4,6,28}*1344a, {28,6,4}*1344a, {14,12,4}*1344a, {2,6,56}*1344, {14,6,8}*1344, {2,12,28}*1344, {2,84,4}*1344a, {4,42,4}*1344a, {2,42,8}*1344
   15-fold covers : {2,18,20}*1440a, {10,18,4}*1440a, {2,90,4}*1440a, {10,6,12}*1440a, {6,6,20}*1440a, {6,6,20}*1440b, {2,6,60}*1440a, {10,6,12}*1440c, {30,6,4}*1440a, {2,30,12}*1440b, {2,6,60}*1440b, {6,30,4}*1440b, {6,30,4}*1440c, {30,6,4}*1440b, {2,30,12}*1440c
   17-fold covers : {2,6,68}*1632a, {34,6,4}*1632a, {2,102,4}*1632a
   18-fold covers : {2,108,4}*1728a, {4,54,4}*1728a, {2,54,8}*1728, {4,6,36}*1728a, {36,6,4}*1728a, {4,18,12}*1728a, {12,18,4}*1728a, {18,12,4}*1728a, {6,36,4}*1728a, {6,36,4}*1728b, {4,6,12}*1728a, {12,6,4}*1728a, {6,12,4}*1728a, {6,12,4}*1728b, {2,6,72}*1728a, {2,18,24}*1728a, {2,6,24}*1728b, {6,18,8}*1728a, {6,18,8}*1728b, {18,6,8}*1728a, {6,6,8}*1728a, {6,6,8}*1728b, {2,12,36}*1728a, {2,36,12}*1728a, {2,36,12}*1728b, {2,12,12}*1728a, {2,12,12}*1728c, {2,18,24}*1728b, {4,18,12}*1728b, {12,18,4}*1728b, {2,6,24}*1728c, {4,6,12}*1728c, {12,6,4}*1728c, {6,6,24}*1728b, {6,6,24}*1728d, {2,6,24}*1728f, {12,6,12}*1728b, {12,6,12}*1728c, {12,6,12}*1728d, {6,12,12}*1728b, {6,12,12}*1728d, {6,12,12}*1728e, {6,12,12}*1728f, {6,6,8}*1728e, {6,6,24}*1728f, {6,6,24}*1728g, {2,12,12}*1728h, {12,6,12}*1728g, {6,12,4}*1728j, {4,6,12}*1728h, {12,6,4}*1728h, {2,12,4}*1728c, {2,12,4}*1728d, {2,6,8}*1728b, {4,6,4}*1728c, {4,6,4}*1728d, {4,12,4}*1728c, {6,12,4}*1728q, {2,12,12}*1728k
   19-fold covers : {2,6,76}*1824a, {38,6,4}*1824a, {2,114,4}*1824a
   20-fold covers : {4,60,4}*1920a, {4,12,20}*1920a, {20,12,4}*1920a, {2,60,8}*1920a, {2,120,4}*1920a, {10,12,8}*1920a, {10,24,4}*1920a, {2,12,40}*1920a, {2,24,20}*1920a, {2,60,8}*1920b, {2,120,4}*1920b, {10,12,8}*1920b, {10,24,4}*1920b, {2,12,40}*1920b, {2,24,20}*1920b, {2,60,4}*1920a, {10,12,4}*1920a, {2,12,20}*1920a, {4,30,8}*1920a, {8,30,4}*1920a, {8,6,20}*1920, {20,6,8}*1920, {4,6,40}*1920a, {40,6,4}*1920a, {2,30,16}*1920, {10,6,16}*1920, {2,6,80}*1920, {4,6,20}*1920a, {2,6,20}*1920a, {10,6,4}*1920b, {20,6,4}*1920b, {4,30,4}*1920b, {2,30,4}*1920b
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);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
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(14)!(1,2);
s1 := Sym(14)!( 5, 6)( 8, 9)(11,12)(13,14);
s2 := Sym(14)!( 3, 5)( 4,11)( 7, 8)( 9,12)(10,13);
s3 := Sym(14)!( 3, 4)( 5, 8)( 6, 9)( 7,10)(11,13)(12,14);
poly := sub<Sym(14)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, 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 >;

to this polytope