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

Small Group ID = [288,958], hypertope number 1.

• Structure of Group

D8 x S3 x S3

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (2,4)(5,9)(6,10)(8,16)(12,18)(13,19)(17,23)(21,24);

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

r2 := (2,5)(4,9)(6,12)(7,14)(10,18)(15,22);

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

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