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

Small Group ID = [288,958], hypertope number 2.

• Structure of Group

D8 x S3 x S3

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (1,2)(3,5)(4,7)(6,11)(8,14)(9,15)(10,19)(12,16)(13,18)(17,22)(20,24)(21,23);

r1 := (1,3)(2,4)(5,10)(6,12)(7,13)(8,16)(9,18)(11,20)(14,21)(15,19)(17,23)(22,24);

r2 := (3,6)(4,8)(5,11)(7,14)(9,17)(15,22);

r3 := (4,9)(7,15)(8,17)(10,18)(13,19)(14,22)(20,23)(21,24);

• 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, (r0*r2)^2, (r3*r2)^2, (r1*r2)^4, (r1*r0*r1*r2)^2, (r1*r3*r1*r2)^2, (r0*r1*r0*r3*r1)^2, r0*r1*r0*(r1*r0*r1*r3)^2*r1, (r3*r1)^6 ];;

• 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 : 12

• This hypertope does not have non-degenerate leaves