Questions?
See the FAQ
or other info.

Polytope of Type {9,2,9,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,2,9,6}*1944
if this polytope has a name.
Group : SmallGroup(1944,2339)
Rank : 5
Schlafli Type : {9,2,9,6}
Number of vertices, edges, etc : 9, 9, 9, 27, 6
Order of s0s1s2s3s4 : 18
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {9,2,9,2}*648, {3,2,9,6}*648, {9,2,3,6}*648
   9-fold quotients : {3,2,9,2}*216, {9,2,3,2}*216, {3,2,3,6}*216
   27-fold quotients : {3,2,3,2}*72
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3)(4,5)(6,7)(8,9);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (11,12)(13,14)(15,18)(16,20)(17,19)(21,24)(22,26)(23,25)(27,30)(28,32)
(29,31)(33,36)(34,35);;
s3 := (10,16)(11,13)(12,22)(14,17)(15,19)(18,28)(20,23)(21,25)(24,33)(26,29)
(27,31)(30,35)(32,34);;
s4 := (13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)(33,34)(35,36);;
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, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(36)!(2,3)(4,5)(6,7)(8,9);
s1 := Sym(36)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(36)!(11,12)(13,14)(15,18)(16,20)(17,19)(21,24)(22,26)(23,25)(27,30)
(28,32)(29,31)(33,36)(34,35);
s3 := Sym(36)!(10,16)(11,13)(12,22)(14,17)(15,19)(18,28)(20,23)(21,25)(24,33)
(26,29)(27,31)(30,35)(32,34);
s4 := Sym(36)!(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)(33,34)(35,36);
poly := sub<Sym(36)|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, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, 
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*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 >; 
 

to this polytope