Polytope of Type {3,2,19}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,19}*228
if this polytope has a name.
Group : SmallGroup(228,8)
Rank : 4
Schlafli Type : {3,2,19}
Number of vertices, edges, etc : 3, 3, 19, 19
Order of s₀s₁s₂s₃ : 57
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,19,2} of size 456
Vertex Figure Of :
   {2,3,2,19} of size 456
   {3,3,2,19} of size 912
   {4,3,2,19} of size 912
   {6,3,2,19} of size 1368
   {4,3,2,19} of size 1824
   {6,3,2,19} of size 1824
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,38}*456, {6,2,19}*456
   3-fold covers : {9,2,19}*684, {3,2,57}*684
   4-fold covers : {12,2,19}*912, {3,2,76}*912, {6,2,38}*912
   5-fold covers : {15,2,19}*1140, {3,2,95}*1140
   6-fold covers : {9,2,38}*1368, {18,2,19}*1368, {3,6,38}*1368, {3,2,114}*1368, {6,2,57}*1368
   7-fold covers : {21,2,19}*1596, {3,2,133}*1596
   8-fold covers : {24,2,19}*1824, {3,2,152}*1824, {12,2,38}*1824, {6,2,76}*1824, {6,4,38}*1824, {3,4,38}*1824
Permutation Representation (GAP) :

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