Polytope of Type {2,19}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,19}*76
if this polytope has a name.
Group : SmallGroup(76,3)
Rank : 3
Schlafli Type : {2,19}
Number of vertices, edges, etc : 2, 19, 19
Order of s₀s₁s₂ : 38
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,19,2} of size 152
Vertex Figure Of :
   {2,2,19} of size 152
   {3,2,19} of size 228
   {4,2,19} of size 304
   {5,2,19} of size 380
   {6,2,19} of size 456
   {7,2,19} of size 532
   {8,2,19} of size 608
   {9,2,19} of size 684
   {10,2,19} of size 760
   {11,2,19} of size 836
   {12,2,19} of size 912
   {13,2,19} of size 988
   {14,2,19} of size 1064
   {15,2,19} of size 1140
   {16,2,19} of size 1216
   {17,2,19} of size 1292
   {18,2,19} of size 1368
   {19,2,19} of size 1444
   {20,2,19} of size 1520
   {21,2,19} of size 1596
   {22,2,19} of size 1672
   {23,2,19} of size 1748
   {24,2,19} of size 1824
   {25,2,19} of size 1900
   {26,2,19} of size 1976
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,38}*152
   3-fold covers : {2,57}*228
   4-fold covers : {2,76}*304, {4,38}*304
   5-fold covers : {2,95}*380
   6-fold covers : {6,38}*456, {2,114}*456
   7-fold covers : {2,133}*532
   8-fold covers : {4,76}*608, {2,152}*608, {8,38}*608
   9-fold covers : {2,171}*684, {6,57}*684
   10-fold covers : {10,38}*760, {2,190}*760
   11-fold covers : {2,209}*836
   12-fold covers : {12,38}*912, {6,76}*912a, {2,228}*912, {4,114}*912a, {6,57}*912, {4,57}*912
   13-fold covers : {2,247}*988
   14-fold covers : {14,38}*1064, {2,266}*1064
   15-fold covers : {2,285}*1140
   16-fold covers : {8,76}*1216a, {4,152}*1216a, {8,76}*1216b, {4,152}*1216b, {4,76}*1216, {16,38}*1216, {2,304}*1216
   17-fold covers : {2,323}*1292
   18-fold covers : {18,38}*1368, {2,342}*1368, {6,114}*1368a, {6,114}*1368b, {6,114}*1368c
   19-fold covers : {2,361}*1444, {38,19}*1444
   20-fold covers : {20,38}*1520, {10,76}*1520, {2,380}*1520, {4,190}*1520
   21-fold covers : {2,399}*1596
   22-fold covers : {22,38}*1672, {2,418}*1672
   23-fold covers : {2,437}*1748
   24-fold covers : {24,38}*1824, {6,152}*1824, {12,76}*1824, {4,228}*1824a, {2,456}*1824, {8,114}*1824, {12,57}*1824, {8,57}*1824, {6,76}*1824, {6,114}*1824, {4,114}*1824
   25-fold covers : {2,475}*1900, {10,95}*1900
   26-fold covers : {26,38}*1976, {2,494}*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);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s1*s0*s1, s0*s2*s0*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*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s1*s0*s1, s0*s2*s0*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*s1*s2 >;

to this polytope