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

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

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

r2 := (1,3)(2,6)(4,9)(5,11)(7,14)(10,18)(12,15)(19,22);

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

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

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