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

Small Group ID = [288,1026], hypertope number 1.

• Structure of Group

(A4 x A4) : C2

• Generators of Automorphism Group (Permutation Representation for GAP)

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

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

r2 := (3,7)(4,8)(5,6)(9,12)(10,11);

r3 := (1,3)(2,5)(4,9)(8,11)(10,12);

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

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

• Number of Elements of each type

type 0: 4 elements

type 1: 24 elements

type 2: 12 elements

type 3: 12 elements

• Order of r₀ r₁ r₂ r₃ : 4

• This hypertope does not have non-degenerate leaves