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

Small Group ID = [324,124], hypertope number 2.

• Structure of Group

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

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (2,4)(5,8)(6,11)(9,17)(10,16)(12,21)(13,22)(14,24)(15,25)(18,20)(19,23)(26,27);

r1 := (1,2)(3,6)(5,9)(7,14)(8,15)(10,20)(12,18)(13,23)(16,21)(17,25)(19,27)(22,26);

r2 := (3,7)(5,10)(6,12)(8,16)(9,18)(11,21)(14,25)(15,24)(17,20);

r3 := (1,3)(2,5)(4,8)(6,13)(9,19)(11,22)(15,26)(17,23)(25,27);

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

• Number of Elements of each type

type 0: 3 elements

type 1: 27 elements

type 2: 9 elements

type 3: 9 elements

• Order of r₀ r₁ r₂ r₃ : 3

• This hypertope does not have non-degenerate leaves