Polytope of Type {2,9,6} with group SmallGroup(216,101)

Overview

Group: SmallGroup(216,101)
Rank: 4
Schläfli Type: {2,9,6}
Vertices, edges, …: 2, 9, 27, 6
Order of s₀s₁s₂s₃: 18
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Degenerate
Universal
Orientable
Flat

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

3-fold

9-fold

{2,3,2}*24

Covers minimal covers in bold

2-fold

{2,18,6}*432b

3-fold

4-fold

5-fold

{2,45,6}*1080

6-fold

7-fold

{2,63,6}*1512

8-fold

9-fold

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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