Polytope of Type {38}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {38}*76
Also Known As : 38-gon, {38}. if this polytope has another name.
Group : SmallGroup(76,3)
Rank : 2
Schlafli Type : {38}
Number of vertices, edges, etc : 38, 38
Order of s₀s₁ : 38
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {38,2} of size 152
   {38,4} of size 304
   {38,6} of size 456
   {38,8} of size 608
   {38,10} of size 760
   {38,12} of size 912
   {38,14} of size 1064
   {38,16} of size 1216
   {38,18} of size 1368
   {38,19} of size 1444
   {38,20} of size 1520
   {38,22} of size 1672
   {38,24} of size 1824
   {38,26} of size 1976
Vertex Figure Of :
   {2,38} of size 152
   {4,38} of size 304
   {6,38} of size 456
   {8,38} of size 608
   {10,38} of size 760
   {12,38} of size 912
   {14,38} of size 1064
   {16,38} of size 1216
   {18,38} of size 1368
   {19,38} of size 1444
   {20,38} of size 1520
   {22,38} of size 1672
   {24,38} of size 1824
   {26,38} of size 1976
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {19}*38
   19-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   2-fold covers : {76}*152
   3-fold covers : {114}*228
   4-fold covers : {152}*304
   5-fold covers : {190}*380
   6-fold covers : {228}*456
   7-fold covers : {266}*532
   8-fold covers : {304}*608
   9-fold covers : {342}*684
   10-fold covers : {380}*760
   11-fold covers : {418}*836
   12-fold covers : {456}*912
   13-fold covers : {494}*988
   14-fold covers : {532}*1064
   15-fold covers : {570}*1140
   16-fold covers : {608}*1216
   17-fold covers : {646}*1292
   18-fold covers : {684}*1368
   19-fold covers : {722}*1444
   20-fold covers : {760}*1520
   21-fold covers : {798}*1596
   22-fold covers : {836}*1672
   23-fold covers : {874}*1748
   24-fold covers : {912}*1824
   25-fold covers : {950}*1900
   26-fold covers : {988}*1976
Permutation Representation (GAP) :

s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)
(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38);;
s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,17)(14,15)(16,21)(18,19)
(20,25)(22,23)(24,29)(26,27)(28,33)(30,31)(32,37)(34,35)(36,38);;
poly := Group([s0,s1]);;

Finitely Presented Group Representation (GAP) :

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

Permutation Representation (Magma) :

s0 := Sym(38)!( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)
(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38);
s1 := Sym(38)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,17)(14,15)(16,21)
(18,19)(20,25)(22,23)(24,29)(26,27)(28,33)(30,31)(32,37)(34,35)(36,38);
poly := sub<Sym(38)|s0,s1>;

Finitely Presented Group Representation (Magma) :

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

References : None.
to this polytope