Polytope of Type {3,2,18,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,18,2}*432
if this polytope has a name.
Group : SmallGroup(432,544)
Rank : 5
Schlafli Type : {3,2,18,2}
Number of vertices, edges, etc : 3, 3, 18, 18, 2
Order of s₀s₁s₂s₃s₄ : 18
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,18,2,2} of size 864
   {3,2,18,2,3} of size 1296
   {3,2,18,2,4} of size 1728
Vertex Figure Of :
   {2,3,2,18,2} of size 864
   {3,3,2,18,2} of size 1728
   {4,3,2,18,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,9,2}*216
   3-fold quotients : {3,2,6,2}*144
   6-fold quotients : {3,2,3,2}*72
   9-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,36,2}*864, {3,2,18,4}*864a, {6,2,18,2}*864
   3-fold covers : {9,2,18,2}*1296, {3,6,18,2}*1296a, {3,2,54,2}*1296, {3,2,18,6}*1296a, {3,2,18,6}*1296b, {3,6,18,2}*1296b
   4-fold covers : {3,2,36,4}*1728a, {3,2,72,2}*1728, {3,2,18,8}*1728, {12,2,18,2}*1728, {6,2,36,2}*1728, {6,2,18,4}*1728a, {6,4,18,2}*1728, {3,4,18,2}*1728, {3,2,18,4}*1728
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := ( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21);;
s3 := ( 4, 8)( 5, 6)( 7,12)( 9,10)(11,16)(13,14)(15,20)(17,18)(19,21);;
s4 := (22,23);;
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*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, 
s3*s4*s3*s4, s0*s1*s0*s1*s0*s1, 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(23)!(2,3);
s1 := Sym(23)!(1,2);
s2 := Sym(23)!( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21);
s3 := Sym(23)!( 4, 8)( 5, 6)( 7,12)( 9,10)(11,16)(13,14)(15,20)(17,18)(19,21);
s4 := Sym(23)!(22,23);
poly := sub<Sym(23)|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*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, s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1, 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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