Polytope of Type {6,3,2}

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

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

Permutation Representation (Magma) :

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

to this polytope