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

Small Group ID = [648,555], hypertope number 1.

• Structure of Group

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

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (1,2)(3,7)(4,6)(5,10)(8,14)(9,13)(11,16)(12,18)(15,17);

r1 := (1,3)(2,5)(4,9)(6,12)(7,10)(8,15)(11,17)(13,16)(14,18);

r2 := (1,2)(3,7)(4,9)(5,10)(6,13)(8,12)(11,17)(14,18)(15,16);

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

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

• Number of Elements of each type

type 0: 6 elements

type 1: 27 elements

type 2: 9 elements

type 3: 18 elements

• Order of r₀ r₁ r₂ r₃ : 6

• This hypertope does not have non-degenerate leaves