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

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

• Structure of Group

S4 x S3

• Generators of Automorphism Group (Permutation Representation for GAP)

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

r1 := (1,2)(3,6)(5,8)(7,10)(11,12);

r2 := (2,4)(5,7)(6,8)(9,11);

r3 := (1,3)(2,5)(4,7)(6,8)(9,11);

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

• Number of Elements of each type

type 0: 4 elements

type 1: 18 elements

type 2: 6 elements

type 3: 4 elements

• Order of r₀ r₁ r₂ r₃ : 12

• This hypertope does not have non-degenerate leaves