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

Small Group ID = [648,555], hypertope number 3.

• 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)(8,12)(9,13)(11,14)(15,17)(16,18);

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

r2 := (1,4)(2,6)(3,8)(7,12)(15,16)(17,18);

r3 := (3,9)(4,10)(5,6)(7,13)(15,16)(17,18);

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

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

• Number of Elements of each type

type 0: 6 elements

type 1: 54 elements

type 2: 9 elements

type 3: 9 elements

• Order of r₀ r₁ r₂ r₃ : 6

• This hypertope does not have non-degenerate leaves