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

Small Group ID = [288,1028], hypertope number 3.

• Structure of Group

C2 x S4 x S3

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (9,12)(14,16)(17,18);

r1 := (1,2)(3,7)(4,9)(5,10)(6,12)(8,14)(11,16)(13,17)(15,18);

r2 := (1,3)(2,5)(4,8)(6,11)(7,10)(9,12)(13,15)(14,17)(16,18);

r3 := (1,4)(2,6)(3,8)(5,11)(7,13)(10,15)(14,18)(16,17);

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

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

• Number of Elements of each type

type 0: 4 elements

type 1: 36 elements

type 2: 6 elements

type 3: 6 elements

• Order of r₀ r₁ r₂ r₃ : 6

• This hypertope does not have non-degenerate leaves