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

Small Group ID = [648,555], hypertope number 8.

• 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)(7,12)(10,16)(11,17)(13,15)(14,18);

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

r2 := (2,5)(4,8)(7,13)(10,16)(11,17)(12,15);

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

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

• 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