Polytope of Type {38,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {38,2}*152
if this polytope has a name.
Group : SmallGroup(152,11)
Rank : 3
Schlafli Type : {38,2}
Number of vertices, edges, etc : 38, 38, 2
Order of s₀s₁s₂ : 38
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {38,2,2} of size 304
   {38,2,3} of size 456
   {38,2,4} of size 608
   {38,2,5} of size 760
   {38,2,6} of size 912
   {38,2,7} of size 1064
   {38,2,8} of size 1216
   {38,2,9} of size 1368
   {38,2,10} of size 1520
   {38,2,11} of size 1672
   {38,2,12} of size 1824
   {38,2,13} of size 1976
Vertex Figure Of :
   {2,38,2} of size 304
   {4,38,2} of size 608
   {6,38,2} of size 912
   {8,38,2} of size 1216
   {10,38,2} of size 1520
   {12,38,2} of size 1824
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {19,2}*76
   19-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {76,2}*304, {38,4}*304
   3-fold covers : {38,6}*456, {114,2}*456
   4-fold covers : {76,4}*608, {152,2}*608, {38,8}*608
   5-fold covers : {38,10}*760, {190,2}*760
   6-fold covers : {38,12}*912, {76,6}*912a, {228,2}*912, {114,4}*912a
   7-fold covers : {38,14}*1064, {266,2}*1064
   8-fold covers : {76,8}*1216a, {152,4}*1216a, {76,8}*1216b, {152,4}*1216b, {76,4}*1216, {38,16}*1216, {304,2}*1216
   9-fold covers : {38,18}*1368, {342,2}*1368, {114,6}*1368a, {114,6}*1368b, {114,6}*1368c
   10-fold covers : {38,20}*1520, {76,10}*1520, {380,2}*1520, {190,4}*1520
   11-fold covers : {38,22}*1672, {418,2}*1672
   12-fold covers : {38,24}*1824, {152,6}*1824, {76,12}*1824, {228,4}*1824a, {456,2}*1824, {114,8}*1824, {76,6}*1824, {114,6}*1824, {114,4}*1824
   13-fold covers : {38,26}*1976, {494,2}*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);;
s2 := (39,40);;
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*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(40)!( 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(40)!( 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);
s2 := Sym(40)!(39,40);
poly := sub<Sym(40)|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*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 >;

to this polytope