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

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)(6,10)(8,13)(9,14)(11,17)(12,18)(15,20)(16,21)(19,22)(23,24);

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

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

r3 := (6,12)(9,16)(10,18)(11,19)(14,21)(15,23)(17,22)(20,24);

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

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

• Number of Elements of each type

type 0: 4 elements

type 1: 36 elements

type 2: 6 elements

type 3: 6 elements

• Order of r₀ r₁ r₂ r₃ : 12

• This hypertope does not have non-degenerate leaves