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Polytope of Type {19,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {19,2}*76
if this polytope has a name.
Group : SmallGroup(76,3)
Rank : 3
Schlafli Type : {19,2}
Number of vertices, edges, etc : 19, 19, 2
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 :
   {19,2,2} of size 152
   {19,2,3} of size 228
   {19,2,4} of size 304
   {19,2,5} of size 380
   {19,2,6} of size 456
   {19,2,7} of size 532
   {19,2,8} of size 608
   {19,2,9} of size 684
   {19,2,10} of size 760
   {19,2,11} of size 836
   {19,2,12} of size 912
   {19,2,13} of size 988
   {19,2,14} of size 1064
   {19,2,15} of size 1140
   {19,2,16} of size 1216
   {19,2,17} of size 1292
   {19,2,18} of size 1368
   {19,2,19} of size 1444
   {19,2,20} of size 1520
   {19,2,21} of size 1596
   {19,2,22} of size 1672
   {19,2,23} of size 1748
   {19,2,24} of size 1824
   {19,2,25} of size 1900
   {19,2,26} of size 1976
Vertex Figure Of :
   {2,19,2} of size 152
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {38,2}*152
   3-fold covers : {57,2}*228
   4-fold covers : {76,2}*304, {38,4}*304
   5-fold covers : {95,2}*380
   6-fold covers : {38,6}*456, {114,2}*456
   7-fold covers : {133,2}*532
   8-fold covers : {76,4}*608, {152,2}*608, {38,8}*608
   9-fold covers : {171,2}*684, {57,6}*684
   10-fold covers : {38,10}*760, {190,2}*760
   11-fold covers : {209,2}*836
   12-fold covers : {38,12}*912, {76,6}*912a, {228,2}*912, {114,4}*912a, {57,6}*912, {57,4}*912
   13-fold covers : {247,2}*988
   14-fold covers : {38,14}*1064, {266,2}*1064
   15-fold covers : {285,2}*1140
   16-fold covers : {76,8}*1216a, {152,4}*1216a, {76,8}*1216b, {152,4}*1216b, {76,4}*1216, {38,16}*1216, {304,2}*1216
   17-fold covers : {323,2}*1292
   18-fold covers : {38,18}*1368, {342,2}*1368, {114,6}*1368a, {114,6}*1368b, {114,6}*1368c
   19-fold covers : {361,2}*1444, {19,38}*1444
   20-fold covers : {38,20}*1520, {76,10}*1520, {380,2}*1520, {190,4}*1520
   21-fold covers : {399,2}*1596
   22-fold covers : {38,22}*1672, {418,2}*1672
   23-fold covers : {437,2}*1748
   24-fold covers : {38,24}*1824, {152,6}*1824, {76,12}*1824, {228,4}*1824a, {456,2}*1824, {114,8}*1824, {57,12}*1824, {57,8}*1824, {76,6}*1824, {114,6}*1824, {114,4}*1824
   25-fold covers : {475,2}*1900, {95,10}*1900
   26-fold covers : {38,26}*1976, {494,2}*1976
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18);;
s2 := (20,21);;
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*s2*s0*s2, s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(21)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19);
s1 := Sym(21)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18);
s2 := Sym(21)!(20,21);
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*s2*s0*s2, s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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