Polytope of Type {2,38,2}

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

s0 := (1,2);;
s1 := ( 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)(39,40);;
s2 := ( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,15)(12,13)(14,19)(16,17)(18,23)(20,21)
(22,27)(24,25)(26,31)(28,29)(30,35)(32,33)(34,39)(36,37)(38,40);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, 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*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(42)!(1,2);
s1 := Sym(42)!( 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)(39,40);
s2 := Sym(42)!( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,15)(12,13)(14,19)(16,17)(18,23)
(20,21)(22,27)(24,25)(26,31)(28,29)(30,35)(32,33)(34,39)(36,37)(38,40);
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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, 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*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