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

Small Group ID = [240,189], hypertope number 1.

• Structure of Group

C2 x S5

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (1,2)(3,5);

r1 := (1,3)(2,4)(5,8)(6,9)(7,10);

r2 := (1,3)(2,5)(4,6)(7,10)(8,9);

r3 := (1,3)(2,5)(4,7)(6,9)(8,10);

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

G := F/[ r0^2, r3^2, r1^2, r2^2, (r3*r0)^2, (r2*r0)^2, (r1*r3)^3, (r2*r1)^3, (r3*r1*r3*r2)^2, (r1*r0*r2)^4, (r1*r0)^6 ];;

• Number of Elements of each type

type 0: 10 elements

type 1: 20 elements

type 2: 5 elements

type 3: 5 elements

• Order of r₀ r₁ r₂ r₃ : 10

• Non-degenerate leaves of Hypertope

Leaf [ 0, 1 ]