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

Small Group ID = [324,124], hypertope number 1.

• 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)(12,20)(13,21)(14,23)(15,24)(18,22)(19,27)(25,26);

r1 := (1,2)(3,6)(5,9)(7,14)(8,15)(10,19)(12,16)(13,22)(17,24)(18,26)(20,27)(21,25);

r2 := (2,4)(3,7)(5,10)(6,12)(8,16)(9,14)(11,20)(13,21)(15,19)(17,23)(18,22)(24,27)(25,26);

r3 := (1,3)(2,5)(4,8)(6,13)(9,18)(10,16)(11,21)(12,20)(14,23)(15,25)(17,22)(19,27)(24,26);

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

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

• 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