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

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)(6,11)(7,10)(8,14)(13,16)(15,17);

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

r2 := (1,3)(2,6)(4,9)(5,11)(7,13)(10,16);

r3 := (1,4)(2,7)(3,9)(5,10)(6,13)(11,16);

• 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, (r3*r2)^2, (r0*r3)^2, (r0*r2)^2, (r1*r0*r1*r3)^2, (r1*r0*r1*r2)^2, r1*r2*(r3*r1)^2*r2*r1*r3, (r1*r0)^6, (r1*r2)^3*r3*(r1*r2)^2*r1*r0*r2*r3*r0 ];;

• 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 : 6

• This hypertope does not have non-degenerate leaves