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

Small Group ID = [216,162], hypertope number 3.

• Structure of Group

S3 x S3 x S3

• Generators of Automorphism Group (Permutation Representation for GAP)

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

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

r2 := (1,2)(3,5)(4,8)(6,11)(7,12)(9,10);

r3 := (1,3)(2,5)(4,9)(6,12)(7,11)(8,10);

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

• Number of Elements of each type

type 0: 3 elements

type 1: 27 elements

type 2: 6 elements

type 3: 6 elements

• Order of r₀ r₁ r₂ r₃ : 6

• This hypertope does not have non-degenerate leaves