Polytope of Type {9,2,18}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,2,18}*648
if this polytope has a name.
Group : SmallGroup(648,296)
Rank : 4
Schlafli Type : {9,2,18}
Number of vertices, edges, etc : 9, 9, 18, 18
Order of s₀s₁s₂s₃ : 18
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {9,2,18,2} of size 1296
Vertex Figure Of :
   {2,9,2,18} of size 1296
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {9,2,9}*324
   3-fold quotients : {3,2,18}*216, {9,2,6}*216
   6-fold quotients : {3,2,9}*108, {9,2,3}*108
   9-fold quotients : {9,2,2}*72, {3,2,6}*72
   18-fold quotients : {3,2,3}*36
   27-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {9,2,36}*1296, {18,2,18}*1296
   3-fold covers : {9,6,18}*1944a, {9,2,54}*1944, {27,2,18}*1944, {9,6,18}*1944b
Permutation Representation (GAP) :

s0 := (2,3)(4,5)(6,7)(8,9);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27);;
s3 := (10,14)(11,12)(13,18)(15,16)(17,22)(19,20)(21,26)(23,24)(25,27);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(27)!(2,3)(4,5)(6,7)(8,9);
s1 := Sym(27)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(27)!(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27);
s3 := Sym(27)!(10,14)(11,12)(13,18)(15,16)(17,22)(19,20)(21,26)(23,24)(25,27);
poly := sub<Sym(27)|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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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 >;

to this polytope