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

Small Group ID = [288,1028], hypertope number 8.

• Structure of Group

C2 x S4 x S3

• Generators of Automorphism Group (Permutation Representation for GAP)

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

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

r2 := (3,6)(4,8)(5,9)(7,11)(10,15)(12,14);

r3 := (3,4)(5,7)(6,8)(9,11)(10,12)(14,15);

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

• Number of Elements of each type

type 0: 6 elements

type 1: 36 elements

type 2: 6 elements

type 3: 4 elements

• Order of r₀ r₁ r₂ r₃ : 12

• This hypertope does not have non-degenerate leaves