Rank 4 Star diagram with parameters (a,b,c) = (4,6,3)

Small Group ID = [144,183], hypertope number 1.

• Structure of Group

S4 x S3

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (1,2)(3,5)(4,7)(6,11)(8,9)(10,12);

r1 := (2,4)(3,6)(5,10)(8,11)(9,12);

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

r3 := (1,3)(2,5)(4,9)(7,8)(10,12);

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

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

• Number of Elements of each type

type 0: 4 elements

type 1: 18 elements

type 2: 6 elements

type 3: 3 elements

• Order of r₀ r₁ r₂ r₃ : 6

• This hypertope does not have non-degenerate leaves