Polytope of Type {2,19,2}

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

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

Permutation Representation (Magma) :

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

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