Rank 4 Star diagram with parameters (a,b,c) = (3,3,3)

Small Group ID = [192,1493], hypertope number 1.

• Structure of Group

(((C2 x C2 x C2) : (C2 x C2)) : C3) : C2

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (3,4)(5,6);

r1 := (2,3)(6,7);

r2 := (1,2)(7,8);

r3 := (3,5)(4,6);

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

r0 := F.1;; r1 := F.2;; r2 := F.3;; r3 := F.4;;

G := F/[ r0^2, r3^2, r1^2, r2^2, (r2*r3)^2, (r2*r0)^2, (r0*r3)^2, (r2*r1)^3, (r1*r3)^3, (r1*r0)^3 ];;

• Number of Elements of each type

type 0: 8 elements

type 1: 24 elements

type 2: 8 elements

type 3: 8 elements

• Order of r₀ r₁ r₂ r₃ : 6

• Non-degenerate leaves of Hypertope

Leaf [ 0, 1 ]

Leaf [ 2, 1 ]

Leaf [ 3, 1 ]