Polytope of Type {2,4,6}

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

s0 := (1,2);;
s1 := ( 4, 7)( 8,11)( 9,12);;
s2 := ( 3, 4)( 5, 9)( 6, 8)( 7,10)(11,14)(12,13);;
s3 := ( 3, 5)( 4, 8)( 7,11)(10,13);;
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*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(14)!(1,2);
s1 := Sym(14)!( 4, 7)( 8,11)( 9,12);
s2 := Sym(14)!( 3, 4)( 5, 9)( 6, 8)( 7,10)(11,14)(12,13);
s3 := Sym(14)!( 3, 5)( 4, 8)( 7,11)(10,13);
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*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope