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

Small Group ID = [648,734], hypertope number 1.

• Structure of Group

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

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (1,2)(3,6)(4,7)(5,10)(8,12)(9,11);

r1 := (2,5)(3,8)(4,10)(6,12);

r2 := (1,3)(2,6)(4,8)(5,11)(7,12)(9,10);

r3 := (1,4)(2,7)(3,9)(6,11);

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

• Number of Elements of each type

type 0: 6 elements

type 1: 27 elements

type 2: 18 elements

type 3: 9 elements

• Order of r₀ r₁ r₂ r₃ : 6

• This hypertope does not have non-degenerate leaves