Polytope of Type {3,9,2}

Atlas Canonical Name {3,9,2}*1296

Overview

Group: SmallGroup(1296,3492)
Rank: 4
Schläfli Type: {3,9,2}
Vertices, edges, …: 36, 162, 108, 2
Order of s₀s₁s₂s₃: 12
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Degenerate
Universal
Orientable
Flat

Quotients maximal quotients in bold

27-fold

{3,3,2}*48

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP)

s0 := ( 2, 3)( 4,19)( 5,21)( 6,20)( 7,10)( 8,12)( 9,11)(13,25)(14,27)(15,26)(17,18)(23,24);;
s1 := ( 2,19)( 3,10)( 4, 7)( 5,25)( 6,16)( 8,22)( 9,13)(11,21)(14,27)(15,18)(17,24)(23,26);;
s2 := ( 1,22)( 2,24)( 3,23)( 5, 6)( 7,13)( 8,15)( 9,14)(10,25)(11,27)(12,26)(17,18)(20,21);;
s3 := (28,29);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(29)!( 2, 3)( 4,19)( 5,21)( 6,20)( 7,10)( 8,12)( 9,11)(13,25)(14,27)(15,26)(17,18)(23,24);
s1 := Sym(29)!( 2,19)( 3,10)( 4, 7)( 5,25)( 6,16)( 8,22)( 9,13)(11,21)(14,27)(15,18)(17,24)(23,26);
s2 := Sym(29)!( 1,22)( 2,24)( 3,23)( 5, 6)( 7,13)( 8,15)( 9,14)(10,25)(11,27)(12,26)(17,18)(20,21);
s3 := Sym(29)!(28,29);
poly := sub<Sym(29)|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, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1 >;