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

Small Group ID = [288,1028], hypertope number 2.

• Structure of Group

C2 x S4 x S3

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (1,2)(3,5)(4,7)(6,9)(8,11)(10,14)(12,15)(13,17)(16,18);

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

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

r3 := (3,6)(4,8)(5,9)(7,11)(10,15)(12,14);

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

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

• Number of Elements of each type

type 0: 8 elements

type 1: 36 elements

type 2: 4 elements

type 3: 6 elements

• Order of r₀ r₁ r₂ r₃ : 12

• This hypertope does not have non-degenerate leaves