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

Small Group ID = [288,1028], hypertope number 1.

• Structure of Group

C2 x S4 x S3

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (2,4)(5,7)(6,8)(9,11)(12,15)(16,18);

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

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

r3 := (1,3)(2,5)(4,7)(6,9)(8,11)(10,13)(12,16)(14,17)(15,18);

• 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, (r0*r2)^2, (r3*r0)^2, (r3*r2)^2, (r2*r1)^3, r2*r1*r0*r1*r2*(r0*r1)^2*r0, (r1*r0*r1*r3*r2)^2, (r1*r3*r2)^4 ];;

• Number of Elements of each type

type 0: 6 elements

type 1: 36 elements

type 2: 4 elements

type 3: 8 elements

• Order of r₀ r₁ r₂ r₃ : 12

• This hypertope does not have non-degenerate leaves