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

Small Group ID = [288,958], hypertope number 3.

• Structure of Group

D8 x S3 x S3

• Generators of Automorphism Group (Permutation Representation for GAP)

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

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

r2 := (1,2)(3,6)(4,8)(5,11)(7,14)(9,17)(10,16)(12,20)(13,19)(15,18)(21,23)(22,24);

r3 := (3,7)(4,9)(5,12)(6,14)(8,17)(11,20);

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

G := F/[ r3^2, r0^2, r1^2, r2^2, (r0*r3)^2, (r2*r0)^2, (r0*r2*r3)^2, (r1*r2*r1*r3)^2, (r1*r3)^4, (r1*r0*r1*r3)^2, (r0*r1*r2*r1)^2, (r0*r1)^6, (r0*r2*r1)^6 ];;

• 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