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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,3,4}*192
if this polytope has a name.
Group : SmallGroup(192,1537)
Rank : 5
Schlafli Type : {2,2,3,4}
Number of vertices, edges, etc : 2, 2, 6, 12, 8
Order of s₀s₁s₂s₃s₄ : 6
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,3,4,2} of size 384
   {2,2,3,4,4} of size 768
   {2,2,3,4,6} of size 1152
   {2,2,3,4,10} of size 1920
Vertex Figure Of :
   {2,2,2,3,4} of size 384
   {3,2,2,3,4} of size 576
   {4,2,2,3,4} of size 768
   {5,2,2,3,4} of size 960
   {6,2,2,3,4} of size 1152
   {7,2,2,3,4} of size 1344
   {9,2,2,3,4} of size 1728
   {10,2,2,3,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,3,4}*96
   4-fold quotients : {2,2,3,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,3,4}*384, {2,2,3,8}*384, {2,2,6,4}*384
   3-fold covers : {2,2,9,4}*576, {2,2,3,12}*576, {2,6,3,4}*576, {6,2,3,4}*576
   4-fold covers : {2,2,3,8}*768, {8,2,3,4}*768, {4,2,3,8}*768, {2,2,12,4}*768b, {2,2,6,4}*768b, {2,2,12,4}*768c, {2,4,6,4}*768a, {4,2,6,4}*768, {2,2,6,8}*768b, {2,2,6,8}*768c, {2,4,3,4}*768
   5-fold covers : {10,2,3,4}*960, {2,2,15,4}*960
   6-fold covers : {4,2,9,4}*1152, {2,2,9,8}*1152, {2,2,18,4}*1152, {12,2,3,4}*1152, {4,2,3,12}*1152, {2,2,3,24}*1152, {2,6,3,8}*1152, {6,2,3,8}*1152, {4,6,3,4}*1152, {2,2,6,12}*1152a, {2,2,6,12}*1152b, {2,6,6,4}*1152a, {2,6,6,4}*1152b, {6,2,6,4}*1152
   7-fold covers : {14,2,3,4}*1344, {2,2,21,4}*1344
   9-fold covers : {2,2,27,4}*1728, {18,2,3,4}*1728, {2,2,9,12}*1728, {2,6,9,4}*1728, {6,2,9,4}*1728, {2,2,3,12}*1728, {6,6,3,4}*1728a, {2,6,3,4}*1728, {6,6,3,4}*1728b, {2,6,3,12}*1728, {6,2,3,12}*1728
   10-fold covers : {20,2,3,4}*1920, {10,2,3,8}*1920, {4,2,15,4}*1920, {2,2,15,8}*1920, {2,2,6,20}*1920a, {2,10,6,4}*1920a, {10,2,6,4}*1920, {2,2,30,4}*1920
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 5, 8)( 6,10);;
s3 := ( 7, 8)( 9,10);;
s4 := (7,9);;
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, s1*s2*s1*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, s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(10)!(1,2);
s1 := Sym(10)!(3,4);
s2 := Sym(10)!( 5, 8)( 6,10);
s3 := Sym(10)!( 7, 8)( 9,10);
s4 := Sym(10)!(7,9);
poly := sub<Sym(10)|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, 
s1*s2*s1*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, s3*s4*s3*s4*s3*s4*s3*s4 >;

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