Polytope of Type {2,2,4,18}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,18}*576a
if this polytope has a name.
Group : SmallGroup(576,5012)
Rank : 5
Schlafli Type : {2,2,4,18}
Number of vertices, edges, etc : 2, 2, 4, 36, 18
Order of s₀s₁s₂s₃s₄ : 36
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,4,18,2} of size 1152
Vertex Figure Of :
   {2,2,2,4,18} of size 1152
   {3,2,2,4,18} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,2,18}*288
   3-fold quotients : {2,2,4,6}*192a
   4-fold quotients : {2,2,2,9}*144
   6-fold quotients : {2,2,2,6}*96
   9-fold quotients : {2,2,4,2}*64
   12-fold quotients : {2,2,2,3}*48
   18-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,4,18}*1152, {2,2,4,36}*1152a, {4,2,4,18}*1152a, {2,2,8,18}*1152
   3-fold covers : {2,2,4,54}*1728a, {2,2,12,18}*1728a, {2,6,4,18}*1728, {6,2,4,18}*1728a, {2,2,12,18}*1728b
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := (23,32)(24,33)(25,34)(26,35)(27,36)(28,37)(29,38)(30,39)(31,40);;
s3 := ( 5,23)( 6,25)( 7,24)( 8,30)( 9,29)(10,31)(11,27)(12,26)(13,28)(14,32)
(15,34)(16,33)(17,39)(18,38)(19,40)(20,36)(21,35)(22,37);;
s4 := ( 5, 8)( 6,10)( 7, 9)(11,12)(14,17)(15,19)(16,18)(20,21)(23,26)(24,28)
(25,27)(29,30)(32,35)(33,37)(34,36)(38,39);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(40)!(1,2);
s1 := Sym(40)!(3,4);
s2 := Sym(40)!(23,32)(24,33)(25,34)(26,35)(27,36)(28,37)(29,38)(30,39)(31,40);
s3 := Sym(40)!( 5,23)( 6,25)( 7,24)( 8,30)( 9,29)(10,31)(11,27)(12,26)(13,28)
(14,32)(15,34)(16,33)(17,39)(18,38)(19,40)(20,36)(21,35)(22,37);
s4 := Sym(40)!( 5, 8)( 6,10)( 7, 9)(11,12)(14,17)(15,19)(16,18)(20,21)(23,26)
(24,28)(25,27)(29,30)(32,35)(33,37)(34,36)(38,39);
poly := sub<Sym(40)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope