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

Small Group ID = [648,555], hypertope number 6.

• Structure of Group

(((C3 x C3) : C3) : (C2 x C2)) x S3

• Generators of Automorphism Group (Permutation Representation for GAP)

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

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

r2 := (2,5)(4,8)(6,9)(7,13)(10,15)(11,16);

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

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

G := F/[ r0^2, r2^2, r1^2, r3^2, (r3*r0)^2, (r2*r0)^2, (r1*r0)^3, (r3*r2*r1*r2*r0*r1)^2, r2*r1*r3*(r1*r2)^2*r3*r2*r3*r1*r3, (r0*(r3*r2)^2)^2*r3*r2*r3*r2, ((r1*r2)^2*r3*r1*r3*r2)^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 : 6

• This hypertope does not have non-degenerate leaves