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

Small Group ID = [288,1028], hypertope number 6.

• Structure of Group

C2 x S3 x S4

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (4,7)(8,11)(12,13);

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

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

r3 := (1,3)(2,5)(8,13)(10,15)(11,12)(14,17);

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

• 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