Polytope of Type {4,2,19}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,19}*304
if this polytope has a name.
Group : SmallGroup(304,31)
Rank : 4
Schlafli Type : {4,2,19}
Number of vertices, edges, etc : 4, 4, 19, 19
Order of s₀s₁s₂s₃ : 76
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,2,19,2} of size 608
Vertex Figure Of :
   {2,4,2,19} of size 608
   {3,4,2,19} of size 912
   {4,4,2,19} of size 1216
   {6,4,2,19} of size 1824
   {3,4,2,19} of size 1824
   {6,4,2,19} of size 1824
   {6,4,2,19} of size 1824
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,19}*152
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,2,19}*608, {4,2,38}*608
   3-fold covers : {12,2,19}*912, {4,2,57}*912
   4-fold covers : {16,2,19}*1216, {4,4,38}*1216, {4,2,76}*1216, {8,2,38}*1216
   5-fold covers : {20,2,19}*1520, {4,2,95}*1520
   6-fold covers : {24,2,19}*1824, {8,2,57}*1824, {12,2,38}*1824, {4,6,38}*1824a, {4,2,114}*1824
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23);;
s3 := ( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(23)!(2,3);
s1 := Sym(23)!(1,2)(3,4);
s2 := Sym(23)!( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23);
s3 := Sym(23)!( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22);
poly := sub<Sym(23)|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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, 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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

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