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

Small Group ID = [648,555], hypertope number 3.

• Structure of Group

(((C3 x C3) : C3) : (C2 x C2)) x S3

• Generators of Automorphism Group (Permutation Representation for GAP)

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

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

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

r3 := (1,5)(2,8)(4,11)(6,14)(7,16)(12,13);

• 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, (r2*r0)^2, (r3*r2)^2, (r2*r0*r3)^2, (r1*r0*r1*r2)^2, r0*r1*r3*r0*r1*r0*r3*r1*r3, r1*r2*(r1*r2*r1*r3)^2*r1*r2, (r3*r1)^6, (r2*r0*(r1*r3)^2*r0*r2*r1*r3*r1)^2 ];;

• Number of Elements of each type

type 0: 9 elements

type 1: 81 elements

type 2: 6 elements

type 3: 9 elements

• Order of r₀ r₁ r₂ r₃ : 6

• This hypertope does not have non-degenerate leaves