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

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

• Structure of Group

A5 : S3

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (1,2)(3,4)(5,7)(6,8)(9,12)(10,13);

r1 := (1,3)(2,5)(4,7)(6,11)(9,14)(10,13);

r2 := (1,2)(3,6)(4,8)(5,9)(7,12)(11,14);

r3 := (1,4)(2,3)(5,10)(6,8)(7,13)(11,15);

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

• Number of Elements of each type

type 0: 3 elements

type 1: 30 elements

type 2: 15 elements

type 3: 15 elements

• Order of r₀ r₁ r₂ r₃ : 15

• This hypertope does not have non-degenerate leaves