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Polytope of Type {4,2,12,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,12,2}*384
if this polytope has a name.
Group : SmallGroup(384,18354)
Rank : 5
Schlafli Type : {4,2,12,2}
Number of vertices, edges, etc : 4, 4, 12, 12, 2
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,2,12,2,2} of size 768
   {4,2,12,2,3} of size 1152
   {4,2,12,2,5} of size 1920
Vertex Figure Of :
   {2,4,2,12,2} of size 768
   {3,4,2,12,2} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,12,2}*192, {4,2,6,2}*192
   3-fold quotients : {4,2,4,2}*128
   4-fold quotients : {4,2,3,2}*96, {2,2,6,2}*96
   6-fold quotients : {2,2,4,2}*64, {4,2,2,2}*64
   8-fold quotients : {2,2,3,2}*48
   12-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,4,12,2}*768, {4,2,12,4}*768a, {8,2,12,2}*768, {4,2,24,2}*768
   3-fold covers : {4,2,36,2}*1152, {4,2,12,6}*1152b, {4,2,12,6}*1152c, {4,6,12,2}*1152b, {4,6,12,2}*1152c, {12,2,12,2}*1152
   5-fold covers : {4,2,60,2}*1920, {4,2,12,10}*1920, {4,10,12,2}*1920, {20,2,12,2}*1920
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 6, 7)( 8, 9)(11,14)(12,13)(15,16);;
s3 := ( 5,11)( 6, 8)( 7,15)( 9,12)(10,13)(14,16);;
s4 := (17,18);;
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, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(18)!(2,3);
s1 := Sym(18)!(1,2)(3,4);
s2 := Sym(18)!( 6, 7)( 8, 9)(11,14)(12,13)(15,16);
s3 := Sym(18)!( 5,11)( 6, 8)( 7,15)( 9,12)(10,13)(14,16);
s4 := Sym(18)!(17,18);
poly := sub<Sym(18)|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, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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