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Polytope of Type {3,2,2,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,2,8}*192
if this polytope has a name.
Group : SmallGroup(192,1313)
Rank : 5
Schlafli Type : {3,2,2,8}
Number of vertices, edges, etc : 3, 3, 2, 8, 8
Order of s0s1s2s3s4 : 24
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,2,8,2} of size 384
   {3,2,2,8,4} of size 768
   {3,2,2,8,4} of size 768
   {3,2,2,8,6} of size 1152
   {3,2,2,8,3} of size 1152
   {3,2,2,8,10} of size 1920
Vertex Figure Of :
   {2,3,2,2,8} of size 384
   {3,3,2,2,8} of size 768
   {4,3,2,2,8} of size 768
   {6,3,2,2,8} of size 1152
   {5,3,2,2,8} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,2,4}*96
   4-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,4,8}*384a, {3,2,2,16}*384, {6,2,2,8}*384
   3-fold covers : {9,2,2,8}*576, {3,2,2,24}*576, {3,2,6,8}*576, {3,6,2,8}*576
   4-fold covers : {3,2,4,8}*768a, {3,2,8,8}*768a, {3,2,8,8}*768b, {3,2,4,16}*768a, {3,2,4,16}*768b, {3,2,2,32}*768, {6,2,4,8}*768a, {6,4,2,8}*768a, {12,2,2,8}*768, {6,2,2,16}*768, {3,4,2,8}*768
   5-fold covers : {3,2,2,40}*960, {3,2,10,8}*960, {15,2,2,8}*960
   6-fold covers : {9,2,4,8}*1152a, {3,6,4,8}*1152a, {3,2,12,8}*1152a, {3,2,4,24}*1152a, {9,2,2,16}*1152, {3,2,6,16}*1152, {3,6,2,16}*1152, {3,2,2,48}*1152, {18,2,2,8}*1152, {6,2,6,8}*1152, {6,6,2,8}*1152a, {6,6,2,8}*1152c, {6,2,2,24}*1152
   7-fold covers : {3,2,2,56}*1344, {3,2,14,8}*1344, {21,2,2,8}*1344
   9-fold covers : {27,2,2,8}*1728, {3,2,2,72}*1728, {9,2,2,24}*1728, {3,2,18,8}*1728, {9,2,6,8}*1728, {9,6,2,8}*1728, {3,6,6,8}*1728a, {3,6,2,8}*1728, {3,2,6,24}*1728a, {3,2,6,24}*1728b, {3,6,2,24}*1728, {3,2,6,24}*1728c, {3,6,6,8}*1728b, {3,2,6,8}*1728
   10-fold covers : {15,2,4,8}*1920a, {3,2,20,8}*1920a, {3,2,4,40}*1920a, {15,2,2,16}*1920, {3,2,10,16}*1920, {3,2,2,80}*1920, {30,2,2,8}*1920, {6,2,10,8}*1920, {6,10,2,8}*1920, {6,2,2,40}*1920
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := (4,5);;
s3 := ( 7, 8)( 9,10)(11,12);;
s4 := ( 6, 7)( 8, 9)(10,11)(12,13);;
poly := Group([s0,s1,s2,s3,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(13)!(2,3);
s1 := Sym(13)!(1,2);
s2 := Sym(13)!(4,5);
s3 := Sym(13)!( 7, 8)( 9,10)(11,12);
s4 := Sym(13)!( 6, 7)( 8, 9)(10,11)(12,13);
poly := sub<Sym(13)|s0,s1,s2,s3,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

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