Rank 4 Star diagram with parameters (a,b,c) = (4,9,4)

Small Group ID = [288,836], hypertope number 1.

• Structure of Group

((C2 x C2 x C2 x C2) : C9) : C2

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (1,2)(3,5)(4,6)(7,9)(16,18)(19,21)(20,22)(23,25)(24,26)(27,29)(28,30)(31,33);

r1 := (1,3)(2,5)(4,8)(6,10)(7,11)(9,13)(12,16)(14,18)(15,19)(17,21)(20,24)(22,26)(23,27)(25,29)(28,32)(30,34)(31,35)(33,36);

r2 := (1,4)(2,6)(3,7)(5,9)(8,12)(10,14)(11,15)(13,17)(16,20)(18,22)(19,23)(21,25)(24,28)(26,30)(27,31)(29,33)(32,35)(34,36);

r3 := (1,5)(2,3)(4,9)(6,7)(16,21)(18,19)(20,25)(22,23)(24,29)(26,27)(28,33)(30,31);

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

G := F/[ r0^2, r3^2, r1^2, r2^2, (r3*r2)^2, (r2*r0)^2, (r0*r3)^2, (r1*r0)^4, r0*r1*r2*r1*r0*r1*r2*r0*r1, r1*r3*r1*r2*(r1*r3)^2*r2, r0*r3*(r1*r0*r3*r1*r2)^2, (r1*r2)^9 ];;

• Number of Elements of each type

type 0: 4 elements

type 1: 36 elements

type 2: 9 elements

type 3: 4 elements

• Order of r₀ r₁ r₂ r₃ : 9

• This hypertope does not have non-degenerate leaves