Polytope of Type {3,2,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,8}*96
if this polytope has a name.
Group : SmallGroup(96,117)
Rank : 4
Schlafli Type : {3,2,8}
Number of vertices, edges, etc : 3, 3, 8, 8
Order of s₀s₁s₂s₃ : 24
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,8,2} of size 192
   {3,2,8,4} of size 384
   {3,2,8,4} of size 384
   {3,2,8,6} of size 576
   {3,2,8,3} of size 576
   {3,2,8,4} of size 768
   {3,2,8,8} of size 768
   {3,2,8,8} of size 768
   {3,2,8,8} of size 768
   {3,2,8,8} of size 768
   {3,2,8,4} of size 768
   {3,2,8,10} of size 960
   {3,2,8,12} of size 1152
   {3,2,8,12} of size 1152
   {3,2,8,3} of size 1152
   {3,2,8,6} of size 1152
   {3,2,8,6} of size 1152
   {3,2,8,6} of size 1152
   {3,2,8,14} of size 1344
   {3,2,8,18} of size 1728
   {3,2,8,9} of size 1728
   {3,2,8,6} of size 1728
   {3,2,8,20} of size 1920
   {3,2,8,20} of size 1920
   {3,2,8,5} of size 1920
   {3,2,8,5} of size 1920
Vertex Figure Of :
   {2,3,2,8} of size 192
   {3,3,2,8} of size 384
   {4,3,2,8} of size 384
   {6,3,2,8} of size 576
   {4,3,2,8} of size 768
   {6,3,2,8} of size 768
   {5,3,2,8} of size 960
   {6,3,2,8} of size 1728
   {5,3,2,8} of size 1920
   {10,3,2,8} of size 1920
   {10,3,2,8} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,4}*48
   4-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,16}*192, {6,2,8}*192
   3-fold covers : {9,2,8}*288, {3,2,24}*288, {3,6,8}*288
   4-fold covers : {3,2,32}*384, {12,2,8}*384, {6,4,8}*384a, {6,2,16}*384, {3,4,8}*384
   5-fold covers : {3,2,40}*480, {15,2,8}*480
   6-fold covers : {9,2,16}*576, {18,2,8}*576, {3,2,48}*576, {3,6,16}*576, {6,2,24}*576, {6,6,8}*576a, {6,6,8}*576c
   7-fold covers : {3,2,56}*672, {21,2,8}*672
   8-fold covers : {3,2,64}*768, {6,4,8}*768a, {6,8,8}*768a, {6,8,8}*768b, {24,2,8}*768, {12,4,8}*768a, {6,4,16}*768a, {6,4,16}*768b, {12,2,16}*768, {6,2,32}*768, {3,8,8}*768, {3,4,16}*768, {6,4,8}*768c
   9-fold covers : {27,2,8}*864, {3,2,72}*864, {9,2,24}*864, {3,6,24}*864a, {9,6,8}*864, {3,6,8}*864a, {3,6,24}*864b, {3,6,8}*864b
   10-fold covers : {3,2,80}*960, {15,2,16}*960, {6,2,40}*960, {6,10,8}*960, {30,2,8}*960
   11-fold covers : {3,2,88}*1056, {33,2,8}*1056
   12-fold covers : {9,2,32}*1152, {3,6,32}*1152, {3,2,96}*1152, {18,4,8}*1152a, {6,12,8}*1152b, {6,12,8}*1152c, {6,4,24}*1152a, {36,2,8}*1152, {12,6,8}*1152b, {12,6,8}*1152c, {12,2,24}*1152, {18,2,16}*1152, {6,6,16}*1152b, {6,6,16}*1152c, {6,2,48}*1152, {9,4,8}*1152, {3,4,24}*1152, {3,6,8}*1152, {3,12,8}*1152
   13-fold covers : {3,2,104}*1248, {39,2,8}*1248
   14-fold covers : {3,2,112}*1344, {21,2,16}*1344, {6,2,56}*1344, {6,14,8}*1344, {42,2,8}*1344
   15-fold covers : {9,2,40}*1440, {45,2,8}*1440, {3,6,40}*1440, {15,2,24}*1440, {3,2,120}*1440, {15,6,8}*1440
   17-fold covers : {3,2,136}*1632, {51,2,8}*1632
   18-fold covers : {27,2,16}*1728, {54,2,8}*1728, {3,2,144}*1728, {9,2,48}*1728, {3,6,48}*1728a, {9,6,16}*1728, {3,6,16}*1728a, {6,2,72}*1728, {18,2,24}*1728, {6,6,24}*1728a, {6,18,8}*1728a, {18,6,8}*1728a, {6,6,8}*1728b, {18,6,8}*1728b, {6,6,8}*1728c, {3,6,48}*1728b, {3,6,16}*1728b, {6,6,24}*1728b, {6,6,24}*1728c, {6,6,24}*1728e, {6,6,8}*1728e, {6,6,24}*1728f, {6,6,8}*1728f, {6,6,8}*1728g
   19-fold covers : {3,2,152}*1824, {57,2,8}*1824
   20-fold covers : {15,2,32}*1920, {3,2,160}*1920, {30,4,8}*1920a, {6,20,8}*1920a, {6,4,40}*1920a, {60,2,8}*1920, {12,10,8}*1920, {12,2,40}*1920, {30,2,16}*1920, {6,10,16}*1920, {6,2,80}*1920, {3,4,40}*1920, {15,4,8}*1920
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

s0 := Sym(11)!(2,3);
s1 := Sym(11)!(1,2);
s2 := Sym(11)!( 5, 6)( 7, 8)( 9,10);
s3 := Sym(11)!( 4, 5)( 6, 7)( 8, 9)(10,11);
poly := sub<Sym(11)|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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope