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

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

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

r2 := (3,6)(4,7)(5,10)(8,11)(9,16)(14,17)(15,20)(18,21)(27,32)(30,33)(31,35)(34,36);

r3 := (3,7)(4,6)(5,11)(8,10)(9,17)(14,16)(15,21)(18,20)(27,33)(30,32)(31,36)(34,35);

• 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, (r2*r3)^2, (r0*r3)^2, (r0*r2)^2, (r3*r1*r2*r1)^2, r2*r1*r2*r0*r1*r2*r1*r0*r1, r1*r3*r0*r1*r3*r1*r0*r1*r3, (r0*r1)^2*r2*r0*r3*(r1*r0)^5*r1*r2*r0*r3*r1 ];;

• Number of Elements of each type

type 0: 9 elements

type 1: 36 elements

type 2: 4 elements

type 3: 4 elements

• Order of r₀ r₁ r₂ r₃ : 9

• This hypertope does not have non-degenerate leaves