Polytope of Type {3,8,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,8,2}*384
if this polytope has a name.
Group : SmallGroup(384,17949)
Rank : 4
Schlafli Type : {3,8,2}
Number of vertices, edges, etc : 12, 48, 32, 2
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,8,2,2} of size 768
   {3,8,2,3} of size 1152
   {3,8,2,5} of size 1920
Vertex Figure Of :
   {2,3,8,2} of size 768
Quotients (Maximal Quotients in Boldface) :
   4-fold quotients : {3,4,2}*96
   8-fold quotients : {3,4,2}*48
   16-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,8,2}*768, {6,8,2}*768a, {3,8,4}*768c, {6,8,2}*768e
   3-fold covers : {9,8,2}*1152, {3,24,2}*1152, {3,8,6}*1152
   5-fold covers : {3,8,10}*1920, {15,8,2}*1920a
Permutation Representation (GAP) :
s0 := ( 1, 9)( 2,10)( 3,11)( 4,12);;
s1 := ( 5, 9)( 6,10)( 7,12)( 8,11);;
s2 := ( 1, 3)( 2, 4)( 5, 6)( 9,11)(10,12);;
s3 := (13,14);;
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, 
s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(14)!( 1, 9)( 2,10)( 3,11)( 4,12);
s1 := Sym(14)!( 5, 9)( 6,10)( 7,12)( 8,11);
s2 := Sym(14)!( 1, 3)( 2, 4)( 5, 6)( 9,11)(10,12);
s3 := Sym(14)!(13,14);
poly := sub<Sym(14)|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, s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >; 
 

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