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

Small Group ID = [288,1028], hypertope number 1.

• Structure of Group

C2 x S4 x S3

• Generators of Automorphism Group (Permutation Representation for GAP)

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

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

r2 := (1,3)(2,6)(4,8)(5,10)(7,12)(11,16);

r3 := (1,4)(2,7)(3,8)(5,11)(6,12)(10,16);

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

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

• Number of Elements of each type

type 0: 6 elements

type 1: 36 elements

type 2: 4 elements

type 3: 6 elements

• Order of r₀ r₁ r₂ r₃ : 6

• This hypertope does not have non-degenerate leaves