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

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

r1 := (1,3)(2,5)(4,9)(6,13)(7,11)(8,12)(10,15)(14,17)(16,18);

r2 := (4,10)(6,14)(8,15)(9,16)(12,17)(13,18);

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

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

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

• Number of Elements of each type

type 0: 3 elements

type 1: 27 elements

type 2: 18 elements

type 3: 18 elements

• Order of r₀ r₁ r₂ r₃ : 18

• This hypertope does not have non-degenerate leaves