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

Small Group ID = [288,889], hypertope number 1.

• Structure of Group

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

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (1,2)(4,6)(8,10);

r1 := (1,3)(2,5)(4,7)(6,9)(8,11)(10,12);

r2 := (1,2)(4,8)(6,10);

r3 := (1,4)(2,6)(8,10);

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

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

• Number of Elements of each type

type 0: 4 elements

type 1: 24 elements

type 2: 9 elements

type 3: 9 elements

• Order of r₀ r₁ r₂ r₃ : 12

• This hypertope does not have non-degenerate leaves