Rank 4 Star diagram with parameters (a,b,c) = (4,6,4)

Small Group ID = [192,1538], hypertope number 2.

• Structure of Group

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

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (1,2)(3,6)(4,5)(7,10)(8,11)(9,12);

r1 := (1,3)(4,8)(5,9)(7,11)(10,12);

r2 := (1,4)(2,5)(3,7)(6,10)(9,12);

r3 := (8,11)(9,12);

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

G := F/[ r3^2, r1^2, r0^2, r2^2, (r2*r3)^2, (r0*r2)^2, (r0*r3)^2, (r0*r1*r3*r1)^2, (r1*r3)^4, (r2*r1*r3)^3, (r2*r1*r0*r1)^2*r0, ((r1*r2)^2*r1*r3)^2, (r2*r1*r2*r0*r1*r2*r1)^2 ];;

• Number of Elements of each type

type 0: 4 elements

type 1: 24 elements

type 2: 6 elements

type 3: 4 elements

• Order of r₀ r₁ r₂ r₃ : 3

• This hypertope does not have non-degenerate leaves