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

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

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

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

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

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

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

• Number of Elements of each type

type 0: 9 elements

type 1: 81 elements

type 2: 6 elements

type 3: 18 elements

• Order of r₀ r₁ r₂ r₃ : 6

• This hypertope does not have non-degenerate leaves