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

Small Group ID = [360,120], hypertope number 1.

• Structure of Group

A5 : S3

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (2,4)(5,6)(8,9)(10,13)(11,14)(12,15);

r1 := (1,2)(3,6)(7,10)(8,11)(9,12)(14,15);

r2 := (1,3)(2,5)(4,6)(8,9)(10,12)(13,15);

r3 := (2,4)(3,7)(5,8)(6,9)(10,12)(13,15);

• 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, (r0*r1)^3, (r3*r2)^3, (r1*r2*r3)^4, r3*(r1*r2*r0)^2*r3*r1*r3*r2*r1*r2*r0 ];;

• Number of Elements of each type

type 0: 5 elements

type 1: 30 elements

type 2: 15 elements

type 3: 10 elements

• Order of r₀ r₁ r₂ r₃ : 15

• This hypertope does not have non-degenerate leaves