Polytope of Type {38,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {38,2,2}*304
if this polytope has a name.
Group : SmallGroup(304,41)
Rank : 4
Schlafli Type : {38,2,2}
Number of vertices, edges, etc : 38, 38, 2, 2
Order of s₀s₁s₂s₃ : 38
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {38,2,2,2} of size 608
   {38,2,2,3} of size 912
   {38,2,2,4} of size 1216
   {38,2,2,5} of size 1520
   {38,2,2,6} of size 1824
Vertex Figure Of :
   {2,38,2,2} of size 608
   {4,38,2,2} of size 1216
   {6,38,2,2} of size 1824
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {19,2,2}*152
   19-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {76,2,2}*608, {38,2,4}*608, {38,4,2}*608
   3-fold covers : {38,2,6}*912, {38,6,2}*912, {114,2,2}*912
   4-fold covers : {38,4,4}*1216, {76,4,2}*1216, {76,2,4}*1216, {38,2,8}*1216, {38,8,2}*1216, {152,2,2}*1216
   5-fold covers : {38,2,10}*1520, {38,10,2}*1520, {190,2,2}*1520
   6-fold covers : {38,2,12}*1824, {38,12,2}*1824, {76,2,6}*1824, {76,6,2}*1824a, {38,4,6}*1824, {38,6,4}*1824a, {228,2,2}*1824, {114,2,4}*1824, {114,4,2}*1824a
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);;
s3 := (41,42);;
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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, 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(42)!( 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(42)!( 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(42)!(39,40);
s3 := Sym(42)!(41,42);
poly := sub<Sym(42)|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*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, 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 >;

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