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

Small Group ID = [120,34], hypertope number 1.

• Structure of Group

S5

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (1,2);

r1 := (2,3);

r2 := (3,4);

r3 := (3,5);

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

• Number of Elements of each type

type 0: 5 elements

type 1: 10 elements

type 2: 5 elements

type 3: 5 elements

• Order of r₀ r₁ r₂ r₃ : 5

• Non-degenerate leaves of Hypertope

Leaf [ 0, 1 ]