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

Small Group ID = [648,704], hypertope number 1.

• Structure of Group

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

• Generators of Automorphism Group (Permutation Representation for GAP)

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

r1 := (1,2)(4,6)(7,9);

r2 := (4,7)(5,8);

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

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

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

• Number of Elements of each type

type 0: 3 elements

type 1: 54 elements

type 2: 27 elements

type 3: 27 elements

• Order of r₀ r₁ r₂ r₃ : 9

• This hypertope does not have non-degenerate leaves