Polytope of Type {9,2,27}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,2,27}*972
if this polytope has a name.
Group : SmallGroup(972,106)
Rank : 4
Schlafli Type : {9,2,27}
Number of vertices, edges, etc : 9, 9, 27, 27
Order of s₀s₁s₂s₃ : 27
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {9,2,27,2} of size 1944
Vertex Figure Of :
   {2,9,2,27} of size 1944
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {9,2,9}*324, {3,2,27}*324
   9-fold quotients : {3,2,9}*108, {9,2,3}*108
   27-fold quotients : {3,2,3}*36
Covers (Minimal Covers in Boldface) :
   2-fold covers : {9,2,54}*1944, {18,2,27}*1944
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)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)
(31,32)(33,34)(35,36);;
s3 := (10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)
(30,31)(32,33)(34,35);;
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*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)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)
(29,30)(31,32)(33,34)(35,36);
s3 := Sym(36)!(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)
(28,29)(30,31)(32,33)(34,35);
poly := sub<Sym(36)|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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope