Rank 4 Tail-triangle diagram with parameters (a,b,c,d) = (3,6,6,3)

Small Group ID = [324,39], hypertope number 1.

• Structure of Group

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

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (2,4)(5,6)(8,9);

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

r2 := (3,7)(5,8)(6,9);

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

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

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

• Number of Elements of each type

type 0: 3 elements

type 1: 27 elements

type 2: 9 elements

type 3: 9 elements

• Order of r₀ r₁ r₂ r₃ : 9

• This hypertope does not have non-degenerate leaves