Polytope of Type {3,4,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,4,2}*96
if this polytope has a name.
Group : SmallGroup(96,226)
Rank : 4
Schlafli Type : {3,4,2}
Number of vertices, edges, etc : 6, 12, 8, 2
Order of s₀s₁s₂s₃ : 6
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,4,2,2} of size 192
   {3,4,2,3} of size 288
   {3,4,2,4} of size 384
   {3,4,2,5} of size 480
   {3,4,2,6} of size 576
   {3,4,2,7} of size 672
   {3,4,2,8} of size 768
   {3,4,2,9} of size 864
   {3,4,2,10} of size 960
   {3,4,2,11} of size 1056
   {3,4,2,12} of size 1152
   {3,4,2,13} of size 1248
   {3,4,2,14} of size 1344
   {3,4,2,15} of size 1440
   {3,4,2,17} of size 1632
   {3,4,2,18} of size 1728
   {3,4,2,19} of size 1824
   {3,4,2,20} of size 1920
Vertex Figure Of :
   {2,3,4,2} of size 192
   {3,3,4,2} of size 384
   {4,3,4,2} of size 384
   {6,3,4,2} of size 576
   {3,3,4,2} of size 768
   {6,3,4,2} of size 768
   {6,3,4,2} of size 768
   {4,3,4,2} of size 768
   {6,3,4,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,4,2}*48
   4-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,4,4}*192b, {3,8,2}*192, {6,4,2}*192
   3-fold covers : {9,4,2}*288, {3,4,6}*288, {3,12,2}*288
   4-fold covers : {3,4,4}*384b, {3,8,2}*384, {3,8,4}*384, {3,4,8}*384, {12,4,2}*384b, {6,4,4}*384d, {6,4,2}*384b, {12,4,2}*384c, {6,8,2}*384b, {6,8,2}*384c
   5-fold covers : {3,4,10}*480, {15,4,2}*480
   6-fold covers : {9,4,4}*576b, {9,8,2}*576, {18,4,2}*576, {3,4,12}*576, {3,24,2}*576, {3,8,6}*576, {3,12,4}*576, {6,4,6}*576b, {6,12,2}*576a, {6,12,2}*576b
   7-fold covers : {3,4,14}*672, {21,4,2}*672
   8-fold covers : {3,8,2}*768, {6,8,2}*768a, {3,8,4}*768a, {3,8,4}*768b, {3,8,8}*768, {3,4,4}*768a, {6,4,4}*768b, {3,8,4}*768c, {3,8,4}*768d, {3,4,4}*768b, {3,4,4}*768c, {3,8,4}*768e, {3,8,4}*768f, {3,4,16}*768, {12,4,2}*768d, {6,4,4}*768e, {12,4,4}*768e, {12,4,4}*768f, {6,8,2}*768d, {6,8,2}*768e, {6,4,4}*768f, {6,4,2}*768a, {12,8,2}*768e, {12,8,2}*768f, {24,4,2}*768c, {24,4,2}*768d, {6,8,4}*768c, {6,8,2}*768f, {12,8,2}*768g, {12,8,2}*768h, {6,4,8}*768c, {6,8,2}*768g, {6,8,4}*768d, {6,4,2}*768b, {24,4,2}*768e, {12,4,2}*768e, {24,4,2}*768f
   9-fold covers : {27,4,2}*864, {3,4,18}*864, {9,4,6}*864, {9,12,2}*864, {3,12,6}*864a, {3,12,2}*864, {3,12,6}*864b
   10-fold covers : {3,4,20}*960, {3,8,10}*960, {15,4,4}*960b, {15,8,2}*960, {6,4,10}*960, {6,20,2}*960c, {30,4,2}*960
   11-fold covers : {3,4,22}*1056, {33,4,2}*1056
   12-fold covers : {9,4,4}*1152b, {9,8,2}*1152, {9,8,4}*1152, {9,4,8}*1152, {36,4,2}*1152b, {18,4,4}*1152d, {18,4,2}*1152b, {36,4,2}*1152c, {18,8,2}*1152b, {18,8,2}*1152c, {3,24,2}*1152, {3,8,12}*1152, {3,4,12}*1152, {3,12,4}*1152a, {3,8,6}*1152, {3,4,24}*1152, {3,12,8}*1152, {3,24,4}*1152, {12,4,6}*1152b, {12,12,2}*1152d, {12,12,2}*1152e, {6,4,12}*1152c, {6,12,2}*1152b, {12,12,2}*1152h, {6,4,6}*1152b, {6,12,4}*1152i, {12,4,6}*1152d, {6,24,2}*1152b, {6,24,2}*1152c, {6,24,2}*1152d, {6,8,6}*1152b, {6,24,2}*1152e, {6,8,6}*1152d, {6,12,4}*1152j, {6,12,2}*1152f, {12,12,2}*1152j, {3,12,2}*1152
   13-fold covers : {3,4,26}*1248, {39,4,2}*1248
   14-fold covers : {3,4,28}*1344, {3,8,14}*1344, {21,4,4}*1344b, {21,8,2}*1344, {6,4,14}*1344, {6,28,2}*1344, {42,4,2}*1344
   15-fold covers : {9,4,10}*1440, {45,4,2}*1440, {3,12,10}*1440, {15,4,6}*1440, {15,12,2}*1440, {3,4,30}*1440
   17-fold covers : {3,4,34}*1632, {51,4,2}*1632
   18-fold covers : {27,4,4}*1728b, {27,8,2}*1728, {54,4,2}*1728, {3,4,36}*1728, {3,8,18}*1728, {9,4,12}*1728, {3,12,12}*1728a, {9,24,2}*1728, {3,24,2}*1728, {9,8,6}*1728, {3,24,6}*1728a, {9,12,4}*1728, {3,12,4}*1728a, {6,4,18}*1728a, {6,36,2}*1728, {18,4,6}*1728b, {18,12,2}*1728a, {18,12,2}*1728b, {6,12,6}*1728b, {6,12,2}*1728a, {6,12,2}*1728b, {3,24,6}*1728b, {3,12,12}*1728b, {3,12,4}*1728b, {6,12,6}*1728i, {6,12,6}*1728j, {6,12,6}*1728k, {6,12,6}*1728l, {6,12,2}*1728c
   19-fold covers : {3,4,38}*1824, {57,4,2}*1824
   20-fold covers : {3,8,20}*1920, {3,4,20}*1920, {3,8,10}*1920, {3,4,40}*1920, {15,4,4}*1920b, {15,8,2}*1920a, {15,8,4}*1920, {15,4,8}*1920, {12,4,10}*1920b, {12,20,2}*1920b, {6,4,20}*1920b, {6,20,2}*1920a, {6,4,10}*1920, {6,20,4}*1920c, {12,4,10}*1920c, {6,40,2}*1920b, {6,8,10}*1920a, {6,40,2}*1920c, {6,8,10}*1920b, {12,20,2}*1920c, {60,4,2}*1920b, {30,4,4}*1920d, {30,4,2}*1920b, {60,4,2}*1920c, {30,8,2}*1920b, {30,8,2}*1920c
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

s0 := Sym(8)!(1,4)(2,6);
s1 := Sym(8)!(3,4)(5,6);
s2 := Sym(8)!(3,5);
s3 := Sym(8)!(7,8);
poly := sub<Sym(8)|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, s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope