Polytope of Type {2,4,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,6}*96c
if this polytope has a name.
Group : SmallGroup(96,226)
Rank : 4
Schlafli Type : {2,4,6}
Number of vertices, edges, etc : 2, 4, 12, 6
Order of s₀s₁s₂s₃ : 6
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,4,6,2} of size 192
   {2,4,6,4} of size 384
   {2,4,6,4} of size 384
   {2,4,6,4} of size 384
   {2,4,6,6} of size 576
   {2,4,6,6} of size 576
   {2,4,6,8} of size 768
   {2,4,6,4} of size 768
   {2,4,6,6} of size 864
   {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
   {2,4,6,14} of size 1344
   {2,4,6,18} of size 1728
   {2,4,6,6} of size 1728
   {2,4,6,6} of size 1728
   {2,4,6,6} of size 1728
   {2,4,6,20} of size 1920
   {2,4,6,20} 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 : {2,4,3}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,12}*192b, {2,4,12}*192c, {2,4,6}*192
   3-fold covers : {2,4,18}*288b
   4-fold covers : {4,4,6}*384b, {2,4,6}*384a, {2,4,24}*384c, {2,4,24}*384d, {2,4,12}*384b, {4,4,6}*384d, {2,4,6}*384b, {2,4,12}*384c, {2,8,6}*384b, {2,8,6}*384c
   5-fold covers : {2,4,30}*480b
   6-fold covers : {2,4,36}*576b, {2,4,36}*576c, {2,4,18}*576, {6,4,6}*576a, {2,12,6}*576a, {2,12,6}*576b
   7-fold covers : {2,4,42}*672b
   8-fold covers : {2,4,12}*768b, {2,4,12}*768c, {4,4,12}*768c, {4,4,12}*768d, {4,4,6}*768c, {2,8,6}*768b, {2,8,6}*768c, {2,4,48}*768c, {2,4,48}*768d, {2,4,12}*768d, {4,4,6}*768e, {4,4,12}*768e, {4,4,12}*768f, {2,8,6}*768d, {2,8,6}*768e, {4,4,6}*768f, {2,4,6}*768a, {2,8,12}*768e, {2,8,12}*768f, {2,4,24}*768c, {2,4,24}*768d, {4,8,6}*768c, {2,8,6}*768f, {2,8,12}*768g, {2,8,12}*768h, {8,4,6}*768c, {2,8,6}*768g, {4,8,6}*768d, {2,4,6}*768b, {2,4,24}*768e, {2,4,12}*768e, {2,4,24}*768f
   9-fold covers : {2,4,54}*864b
   10-fold covers : {2,4,60}*960b, {2,4,60}*960c, {10,4,6}*960, {2,20,6}*960c, {2,4,30}*960
   11-fold covers : {2,4,66}*1056b
   12-fold covers : {4,4,18}*1152b, {2,4,18}*1152a, {2,4,72}*1152c, {2,4,72}*1152d, {2,4,36}*1152b, {4,4,18}*1152d, {2,4,18}*1152b, {2,4,36}*1152c, {2,8,18}*1152b, {2,8,18}*1152c, {6,4,12}*1152b, {2,12,12}*1152f, {2,12,12}*1152g, {12,4,6}*1152c, {2,12,6}*1152b, {2,12,12}*1152i, {4,12,6}*1152g, {6,4,6}*1152a, {6,4,12}*1152d, {2,24,6}*1152b, {2,24,6}*1152c, {2,24,6}*1152d, {6,8,6}*1152a, {2,24,6}*1152e, {6,8,6}*1152c, {4,12,6}*1152j, {2,12,6}*1152f, {2,12,12}*1152k
   13-fold covers : {2,4,78}*1248b
   14-fold covers : {2,4,84}*1344b, {2,4,84}*1344c, {14,4,6}*1344, {2,28,6}*1344, {2,4,42}*1344
   15-fold covers : {2,4,90}*1440b
   17-fold covers : {2,4,102}*1632b
   18-fold covers : {2,4,108}*1728b, {2,4,108}*1728c, {2,4,54}*1728, {18,4,6}*1728a, {2,36,6}*1728, {6,4,18}*1728b, {2,12,18}*1728a, {2,12,18}*1728b, {6,12,6}*1728a, {2,12,6}*1728a, {2,12,6}*1728b, {2,12,12}*1728o, {6,12,6}*1728e, {6,12,6}*1728f, {6,12,6}*1728g, {6,12,6}*1728h, {2,12,6}*1728c
   19-fold covers : {2,4,114}*1824b
   20-fold covers : {4,4,30}*1920b, {2,4,30}*1920a, {2,4,120}*1920c, {2,4,120}*1920d, {10,4,12}*1920b, {2,20,12}*1920b, {20,4,6}*1920b, {2,20,6}*1920a, {4,20,6}*1920c, {10,4,6}*1920, {10,4,12}*1920c, {2,40,6}*1920b, {10,8,6}*1920a, {2,40,6}*1920c, {10,8,6}*1920b, {2,20,12}*1920c, {2,4,60}*1920b, {4,4,30}*1920d, {2,4,30}*1920b, {2,4,60}*1920c, {2,8,30}*1920b, {2,8,30}*1920c
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope