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

Small Group ID = [648,299], hypertope number 1.

• Structure of Group

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

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (1,2)(3,4)(5,9)(6,8)(7,12)(10,15)(11,16)(13,17)(14,18);

r1 := (3,5)(4,7)(10,17)(11,18)(13,15)(14,16);

r2 := (1,2)(3,6)(4,8)(5,10)(7,13)(9,15)(11,14)(12,17)(16,18);

r3 := (1,3)(2,4)(5,11)(6,8)(7,14)(9,16)(10,13)(12,18)(15,17);

• 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, (r2*r0)^2, (r3*r2)^3, (r3*r2*r1*r2)^2, (r2*r1)^2*r2*r0*r1*r2*r1*r0, (r2*r1)^6, (r0*r1)^6 ];;

• Number of Elements of each type

type 0: 6 elements

type 1: 54 elements

type 2: 9 elements

type 3: 9 elements

• Order of r₀ r₁ r₂ r₃ : 18

• This hypertope does not have non-degenerate leaves