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

Small Group ID = [288,1028], hypertope number 5.

• 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 := (3,4)(5,7)(6,8)(9,11)(13,16)(17,18);

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

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

G := F/[ r3^2, r2^2, r0^2, r1^2, (r0*r3)^2, (r0*r2)^2, (r2*r3)^2, (r1*r2*r1*r3)^2, (r0*r1*r2*r1)^2*r2, ((r1*r3)^2*r0)^2, (r1*r3*(r1*r0)^2)^2, ((r1*r0)^3*r2)^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