Polytope of Type {2,4,3,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,3,4}*192
if this polytope has a name.
Group : SmallGroup(192,1538)
Rank : 5
Schlafli Type : {2,4,3,4}
Number of vertices, edges, etc : 2, 4, 6, 6, 4
Order of s₀s₁s₂s₃s₄ : 6
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,4,3,4,2} of size 384
Vertex Figure Of :
   {2,2,4,3,4} of size 384
   {3,2,4,3,4} of size 576
   {4,2,4,3,4} of size 768
   {5,2,4,3,4} of size 960
   {6,2,4,3,4} of size 1152
   {7,2,4,3,4} of size 1344
   {9,2,4,3,4} of size 1728
   {10,2,4,3,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,3,4}*384a, {2,4,3,4}*384b, {2,4,6,4}*384d, {2,4,6,4}*384e, {2,4,6,4}*384f, {2,4,6,4}*384g
   3-fold covers : {2,4,9,4}*576
   4-fold covers : {4,4,3,4}*768a, {4,4,3,4}*768b, {2,4,12,4}*768f, {2,4,12,4}*768g, {2,4,12,4}*768h, {2,4,12,4}*768i, {2,4,3,8}*768, {2,8,3,4}*768, {2,4,3,4}*768, {2,4,6,4}*768c, {2,4,6,4}*768d, {2,4,6,4}*768e, {2,4,6,4}*768f
   5-fold covers : {2,4,15,4}*960
   6-fold covers : {2,4,9,4}*1152a, {2,4,9,4}*1152b, {2,4,18,4}*1152d, {2,4,18,4}*1152e, {2,4,18,4}*1152f, {2,4,18,4}*1152g, {2,4,3,12}*1152, {2,4,6,12}*1152f, {2,12,3,4}*1152, {2,12,6,4}*1152f, {6,4,3,4}*1152
   7-fold covers : {2,4,21,4}*1344
   9-fold covers : {2,4,27,4}*1728
   10-fold covers : {2,4,6,20}*1920c, {10,4,3,4}*1920, {2,20,6,4}*1920c, {2,4,15,4}*1920a, {2,4,15,4}*1920b, {2,4,30,4}*1920d, {2,4,30,4}*1920e, {2,4,30,4}*1920f, {2,4,30,4}*1920g
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 3, 4)( 5, 8)( 6, 7)( 9,16)(10,17)(11,12)(13,15)(14,18);;
s2 := ( 4, 6)( 5, 9)( 8,13)(11,16)(12,15)(14,17);;
s3 := ( 5,10)( 6, 7)( 8,17)(11,18)(12,14)(13,15);;
s4 := ( 3,10)( 4,17)( 5, 9)( 6,14)( 7,18)( 8,16)(11,13)(12,15);;
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, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4, s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s2*s4*s3*s2*s4*s3*s2*s4*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(18)!(1,2);
s1 := Sym(18)!( 3, 4)( 5, 8)( 6, 7)( 9,16)(10,17)(11,12)(13,15)(14,18);
s2 := Sym(18)!( 4, 6)( 5, 9)( 8,13)(11,16)(12,15)(14,17);
s3 := Sym(18)!( 5,10)( 6, 7)( 8,17)(11,18)(12,14)(13,15);
s4 := Sym(18)!( 3,10)( 4,17)( 5, 9)( 6,14)( 7,18)( 8,16)(11,13)(12,15);
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*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s1*s2*s3*s1*s2*s3*s1*s2, s2*s4*s3*s2*s4*s3*s2*s4*s3 >;

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