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

Small Group ID = [648,555], hypertope number 2.

• Structure of Group

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

• Generators of Automorphism Group (Permutation Representation for GAP)

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

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

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

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

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

• Number of Elements of each type

type 0: 9 elements

type 1: 81 elements

type 2: 9 elements

type 3: 6 elements

• Order of r₀ r₁ r₂ r₃ : 6

• This hypertope does not have non-degenerate leaves