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

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

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

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

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

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

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

• 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