Polytope of Type {6,4,2}

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

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

Permutation Representation (Magma) :

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

to this polytope