Polytope of Type {2,2,19}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,19}*152
if this polytope has a name.
Group : SmallGroup(152,11)
Rank : 4
Schlafli Type : {2,2,19}
Number of vertices, edges, etc : 2, 2, 19, 19
Order of s₀s₁s₂s₃ : 38
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,19,2} of size 304
Vertex Figure Of :
   {2,2,2,19} of size 304
   {3,2,2,19} of size 456
   {4,2,2,19} of size 608
   {5,2,2,19} of size 760
   {6,2,2,19} of size 912
   {7,2,2,19} of size 1064
   {8,2,2,19} of size 1216
   {9,2,2,19} of size 1368
   {10,2,2,19} of size 1520
   {11,2,2,19} of size 1672
   {12,2,2,19} of size 1824
   {13,2,2,19} of size 1976
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,19}*304, {2,2,38}*304
   3-fold covers : {6,2,19}*456, {2,2,57}*456
   4-fold covers : {8,2,19}*608, {2,2,76}*608, {2,4,38}*608, {4,2,38}*608
   5-fold covers : {10,2,19}*760, {2,2,95}*760
   6-fold covers : {12,2,19}*912, {4,2,57}*912, {2,6,38}*912, {6,2,38}*912, {2,2,114}*912
   7-fold covers : {14,2,19}*1064, {2,2,133}*1064
   8-fold covers : {16,2,19}*1216, {4,4,38}*1216, {2,4,76}*1216, {4,2,76}*1216, {2,8,38}*1216, {8,2,38}*1216, {2,2,152}*1216
   9-fold covers : {18,2,19}*1368, {2,2,171}*1368, {2,6,57}*1368, {6,2,57}*1368
   10-fold covers : {20,2,19}*1520, {4,2,95}*1520, {2,10,38}*1520, {10,2,38}*1520, {2,2,190}*1520
   11-fold covers : {22,2,19}*1672, {2,2,209}*1672
   12-fold covers : {24,2,19}*1824, {8,2,57}*1824, {2,12,38}*1824, {12,2,38}*1824, {2,6,76}*1824a, {6,2,76}*1824, {4,6,38}*1824a, {6,4,38}*1824, {2,2,228}*1824, {2,4,114}*1824a, {4,2,114}*1824, {2,6,57}*1824, {2,4,57}*1824
   13-fold covers : {26,2,19}*1976, {2,2,247}*1976
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);;
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*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*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*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(23)!(1,2);
s1 := Sym(23)!(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*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*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*s2*s3 >;

to this polytope