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

Small Group ID = [96,227], hypertope number 1.

• Structure of Group

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

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (1,2)(3,5)(4,6)(7,8);

r1 := (1,2)(3,7)(4,5)(6,8);

r2 := (1,3)(2,5)(4,7)(6,8);

r3 := (1,4)(2,6)(3,7)(5,8);

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

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

• Number of Elements of each type

type 0: 4 elements

type 1: 12 elements

type 2: 4 elements

type 3: 4 elements

• Order of r₀ r₁ r₂ r₃ : 3

• This hypertope does not have non-degenerate leaves