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Polytope of Type {12,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6,2}*384a
if this polytope has a name.
Group : SmallGroup(384,20051)
Rank : 4
Schlafli Type : {12,6,2}
Number of vertices, edges, etc : 16, 48, 8, 2
Order of s0s1s2s3 : 4
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {12,6,2,2} of size 768
   {12,6,2,3} of size 1152
   {12,6,2,5} of size 1920
Vertex Figure Of :
   {2,12,6,2} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,6,2}*192
   4-fold quotients : {3,6,2}*96, {6,3,2}*96
   8-fold quotients : {3,3,2}*48
   12-fold quotients : {4,2,2}*32
   24-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,12,2}*768a, {12,6,4}*768a, {12,6,2}*768, {12,12,2}*768d, {24,6,2}*768a, {24,6,2}*768b
   3-fold covers : {12,6,2}*1152a, {12,6,6}*1152b, {12,6,2}*1152e
   5-fold covers : {60,6,2}*1920a, {12,6,10}*1920a, {12,30,2}*1920b
Permutation Representation (GAP) :
s0 := ( 1, 5)( 2, 6)( 7,12)( 8,11)( 9,10);;
s1 := ( 1, 7)( 2, 8)( 3,11)( 4,12)( 5, 9)( 6,10);;
s2 := ( 1, 5)( 2, 6)( 3, 4)( 7,11)( 8,12)( 9,10);;
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, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(14)!( 1, 5)( 2, 6)( 7,12)( 8,11)( 9,10);
s1 := Sym(14)!( 1, 7)( 2, 8)( 3,11)( 4,12)( 5, 9)( 6,10);
s2 := Sym(14)!( 1, 5)( 2, 6)( 3, 4)( 7,11)( 8,12)( 9,10);
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, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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