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

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

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