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

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)(3,4)(5,6)(7,8)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32);

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

r2 := (1,4)(2,3)(5,8)(6,7)(17,20)(18,19)(21,24)(22,23)(25,28)(26,27)(29,32)(30,31);

r3 := (1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)(17,21)(18,22)(19,23)(20,24)(25,29)(26,30)(27,31)(28,32)(33,35)(34,36);

• 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*r2*r1*r3*(r1*r2)^2*r3, r0*(r1*r0*r1*r3)^2, r1*r0*r2*r1*r3*(r0*r2*r1)^2*r3, (r1*r3)^9 ];;

• Number of Elements of each type

type 0: 4 elements

type 1: 36 elements

type 2: 4 elements

type 3: 9 elements

• Order of r₀ r₁ r₂ r₃ : 9

• This hypertope does not have non-degenerate leaves