Polytope of Type {2,2,19,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,19,2}*304
if this polytope has a name.
Group : SmallGroup(304,41)
Rank : 5
Schlafli Type : {2,2,19,2}
Number of vertices, edges, etc : 2, 2, 19, 19, 2
Order of s₀s₁s₂s₃s₄ : 38
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,19,2,2} of size 608
   {2,2,19,2,3} of size 912
   {2,2,19,2,4} of size 1216
   {2,2,19,2,5} of size 1520
   {2,2,19,2,6} of size 1824
Vertex Figure Of :
   {2,2,2,19,2} of size 608
   {3,2,2,19,2} of size 912
   {4,2,2,19,2} of size 1216
   {5,2,2,19,2} of size 1520
   {6,2,2,19,2} of size 1824
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,19,2}*608, {2,2,38,2}*608
   3-fold covers : {6,2,19,2}*912, {2,2,57,2}*912
   4-fold covers : {8,2,19,2}*1216, {2,2,38,4}*1216, {2,4,38,2}*1216, {4,2,38,2}*1216, {2,2,76,2}*1216
   5-fold covers : {10,2,19,2}*1520, {2,2,95,2}*1520
   6-fold covers : {12,2,19,2}*1824, {4,2,57,2}*1824, {2,2,38,6}*1824, {2,6,38,2}*1824, {6,2,38,2}*1824, {2,2,114,2}*1824
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (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);;
s4 := (24,25);;
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, s3*s4*s3*s4, 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(25)!(1,2);
s1 := Sym(25)!(3,4);
s2 := Sym(25)!( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23);
s3 := Sym(25)!( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22);
s4 := Sym(25)!(24,25);
poly := sub<Sym(25)|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, 
s3*s4*s3*s4, 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 >;

to this polytope