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

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

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

Permutation Representation (Magma) :

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

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