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

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

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

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

r3 := (1,5)(2,8)(3,4)(6,13)(7,9)(10,17)(11,20)(12,15)(14,22)(16,23)(18,19)(21,24);

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

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