Polytope of Type {4,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,2}*96a
if this polytope has a name.
Group : SmallGroup(96,209)
Rank : 4
Schlafli Type : {4,6,2}
Number of vertices, edges, etc : 4, 12, 6, 2
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,6,2,2} of size 192
   {4,6,2,3} of size 288
   {4,6,2,4} of size 384
   {4,6,2,5} of size 480
   {4,6,2,6} of size 576
   {4,6,2,7} of size 672
   {4,6,2,8} of size 768
   {4,6,2,9} of size 864
   {4,6,2,10} of size 960
   {4,6,2,11} of size 1056
   {4,6,2,12} of size 1152
   {4,6,2,13} of size 1248
   {4,6,2,14} of size 1344
   {4,6,2,15} of size 1440
   {4,6,2,17} of size 1632
   {4,6,2,18} of size 1728
   {4,6,2,19} of size 1824
   {4,6,2,20} of size 1920
Vertex Figure Of :
   {2,4,6,2} of size 192
   {4,4,6,2} of size 384
   {6,4,6,2} of size 576
   {3,4,6,2} of size 576
   {8,4,6,2} of size 768
   {8,4,6,2} of size 768
   {4,4,6,2} of size 768
   {6,4,6,2} of size 864
   {10,4,6,2} of size 960
   {12,4,6,2} of size 1152
   {6,4,6,2} of size 1152
   {14,4,6,2} of size 1344
   {5,4,6,2} of size 1440
   {18,4,6,2} of size 1728
   {9,4,6,2} of size 1728
   {4,4,6,2} of size 1728
   {6,4,6,2} of size 1728
   {20,4,6,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,6,2}*48
   3-fold quotients : {4,2,2}*32
   4-fold quotients : {2,3,2}*24
   6-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,12,2}*192a, {4,6,4}*192a, {8,6,2}*192
   3-fold covers : {4,18,2}*288a, {12,6,2}*288a, {4,6,6}*288a, {4,6,6}*288b, {12,6,2}*288c
   4-fold covers : {4,12,4}*384a, {4,24,2}*384a, {4,12,2}*384a, {4,24,2}*384b, {8,12,2}*384a, {8,12,2}*384b, {4,6,8}*384a, {8,6,4}*384a, {16,6,2}*384, {4,6,4}*384a, {4,6,2}*384b
   5-fold covers : {20,6,2}*480a, {4,6,10}*480a, {4,30,2}*480a
   6-fold covers : {4,36,2}*576a, {4,18,4}*576a, {8,18,2}*576, {4,12,6}*576a, {4,12,6}*576b, {4,6,12}*576a, {12,6,4}*576a, {24,6,2}*576a, {8,6,6}*576a, {8,6,6}*576b, {12,12,2}*576a, {12,12,2}*576b, {24,6,2}*576c, {4,6,12}*576c, {12,6,4}*576c
   7-fold covers : {28,6,2}*672a, {4,6,14}*672a, {4,42,2}*672a
   8-fold covers : {8,12,2}*768a, {4,24,2}*768a, {8,24,2}*768a, {8,24,2}*768b, {8,24,2}*768c, {8,24,2}*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, {16,12,2}*768a, {4,48,2}*768a, {16,12,2}*768b, {4,48,2}*768b, {4,12,2}*768a, {4,24,2}*768b, {8,12,2}*768b, {4,6,16}*768a, {16,6,4}*768a, {32,6,2}*768, {4,12,4}*768e, {4,12,2}*768d, {4,6,4}*768c, {4,6,4}*768d, {4,12,4}*768g, {8,6,2}*768f, {8,6,4}*768a, {8,6,2}*768g, {4,6,8}*768b, {4,6,8}*768c, {4,6,2}*768b, {4,12,2}*768e
   9-fold covers : {4,54,2}*864a, {36,6,2}*864a, {12,18,2}*864a, {12,6,2}*864b, {4,6,18}*864a, {4,18,6}*864a, {4,18,6}*864b, {4,6,6}*864a, {4,6,6}*864b, {12,18,2}*864b, {12,6,2}*864c, {12,6,6}*864b, {12,6,6}*864c, {12,6,2}*864g, {4,6,6}*864h, {12,6,6}*864f, {12,6,6}*864g, {4,6,2}*864b
   10-fold covers : {4,12,10}*960a, {4,6,20}*960a, {20,6,4}*960a, {40,6,2}*960, {8,6,10}*960, {20,12,2}*960, {4,60,2}*960a, {4,30,4}*960a, {8,30,2}*960
   11-fold covers : {44,6,2}*1056a, {4,6,22}*1056a, {4,66,2}*1056a
   12-fold covers : {4,36,4}*1152a, {4,12,12}*1152a, {4,12,12}*1152b, {12,12,4}*1152a, {12,12,4}*1152b, {8,36,2}*1152a, {4,72,2}*1152a, {8,12,6}*1152a, {8,12,6}*1152b, {4,24,6}*1152b, {4,24,6}*1152c, {12,24,2}*1152a, {12,24,2}*1152b, {24,12,2}*1152a, {24,12,2}*1152c, {8,36,2}*1152b, {4,72,2}*1152b, {8,12,6}*1152d, {8,12,6}*1152e, {4,24,6}*1152e, {4,24,6}*1152f, {12,24,2}*1152d, {12,24,2}*1152e, {24,12,2}*1152d, {24,12,2}*1152f, {4,36,2}*1152a, {4,12,6}*1152a, {4,12,6}*1152b, {12,12,2}*1152a, {12,12,2}*1152b, {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, {16,18,2}*1152, {16,6,6}*1152a, {16,6,6}*1152b, {48,6,2}*1152a, {48,6,2}*1152b, {4,18,4}*1152a, {4,18,2}*1152b, {12,12,2}*1152d, {12,6,4}*1152a, {12,6,2}*1152b, {4,6,6}*1152c, {4,6,6}*1152d, {4,6,6}*1152e, {4,6,12}*1152b, {4,6,12}*1152c, {4,12,6}*1152g, {12,6,4}*1152d, {12,6,2}*1152e, {12,6,2}*1152f
   13-fold covers : {52,6,2}*1248a, {4,6,26}*1248a, {4,78,2}*1248a
   14-fold covers : {4,6,28}*1344a, {28,6,4}*1344a, {4,12,14}*1344a, {56,6,2}*1344, {8,6,14}*1344, {28,12,2}*1344, {4,84,2}*1344a, {4,42,4}*1344a, {8,42,2}*1344
   15-fold covers : {20,18,2}*1440a, {4,18,10}*1440a, {4,90,2}*1440a, {12,6,10}*1440a, {20,6,6}*1440a, {20,6,6}*1440b, {60,6,2}*1440a, {12,6,10}*1440c, {4,6,30}*1440a, {12,30,2}*1440b, {60,6,2}*1440b, {4,6,30}*1440b, {4,30,6}*1440b, {4,30,6}*1440c, {12,30,2}*1440c
   17-fold covers : {68,6,2}*1632a, {4,6,34}*1632a, {4,102,2}*1632a
   18-fold covers : {4,108,2}*1728a, {4,54,4}*1728a, {8,54,2}*1728, {4,6,36}*1728a, {36,6,4}*1728a, {4,18,12}*1728a, {12,18,4}*1728a, {4,12,18}*1728a, {4,36,6}*1728a, {4,36,6}*1728b, {4,6,12}*1728a, {12,6,4}*1728a, {4,12,6}*1728a, {4,12,6}*1728b, {72,6,2}*1728a, {24,18,2}*1728a, {24,6,2}*1728b, {8,6,18}*1728a, {8,18,6}*1728a, {8,18,6}*1728b, {8,6,6}*1728a, {8,6,6}*1728b, {12,36,2}*1728a, {12,36,2}*1728b, {36,12,2}*1728a, {12,12,2}*1728b, {12,12,2}*1728c, {24,18,2}*1728b, {4,18,12}*1728b, {12,18,4}*1728b, {24,6,2}*1728c, {4,6,12}*1728c, {12,6,4}*1728c, {24,6,6}*1728b, {24,6,6}*1728c, {24,6,2}*1728f, {12,6,12}*1728b, {12,6,12}*1728c, {12,6,12}*1728d, {12,12,6}*1728b, {12,12,6}*1728c, {12,12,6}*1728d, {12,12,6}*1728e, {8,6,6}*1728e, {24,6,6}*1728f, {24,6,6}*1728g, {12,12,2}*1728h, {12,6,12}*1728g, {4,12,6}*1728j, {4,6,12}*1728h, {12,6,4}*1728h, {4,12,2}*1728c, {4,12,2}*1728d, {8,6,2}*1728b, {4,6,4}*1728c, {4,6,4}*1728d, {4,12,4}*1728d, {4,12,6}*1728q, {12,12,2}*1728l
   19-fold covers : {76,6,2}*1824a, {4,6,38}*1824a, {4,114,2}*1824a
   20-fold covers : {4,60,4}*1920a, {4,12,20}*1920a, {20,12,4}*1920a, {8,60,2}*1920a, {4,120,2}*1920a, {8,12,10}*1920a, {4,24,10}*1920a, {40,12,2}*1920a, {20,24,2}*1920a, {8,60,2}*1920b, {4,120,2}*1920b, {8,12,10}*1920b, {4,24,10}*1920b, {40,12,2}*1920b, {20,24,2}*1920b, {4,60,2}*1920a, {4,12,10}*1920a, {20,12,2}*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, {16,30,2}*1920, {16,6,10}*1920, {80,6,2}*1920, {20,6,4}*1920a, {20,6,2}*1920a, {4,6,10}*1920b, {4,6,20}*1920b, {4,30,4}*1920a, {4,30,2}*1920b
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);;
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*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(14)!( 2, 5)( 6, 9)( 7,10);
s1 := Sym(14)!( 1, 2)( 3, 7)( 4, 6)( 5, 8)( 9,12)(10,11);
s2 := Sym(14)!( 1, 3)( 2, 6)( 5, 9)( 8,11);
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*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 >;

to this polytope