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

Small Group ID = [192,1147], hypertope number 1.

• Structure of Group

((C2 x C2 x C2 x C2) : C2) x S3

• Generators of Automorphism Group (Permutation Representation for GAP)

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

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

r2 := (3,6)(4,8)(5,10)(7,13)(11,16)(14,18)(15,19)(17,21);

r3 := (3,4)(5,7)(6,8)(10,13)(20,22)(23,24);

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

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

• Number of Elements of each type

type 0: 4 elements

type 1: 24 elements

type 2: 6 elements

type 3: 4 elements

• Order of r₀ r₁ r₂ r₃ : 12

• This hypertope does not have non-degenerate leaves