Rank 4 Star diagram with parameters (a,b,c) = (9,6,6)

Small Group ID = [648,554], hypertope number 2.

• Structure of Group

D18 x S3 x S3

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (2,5)(6,12)(7,13)(8,17)(10,21)(11,18)(14,23)(15,22)(16,27)(19,29)(20,31)(24,30)(25,26)(28,33)(32,34)(35,36);

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

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

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

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

G := F/[ r1^2, r0^2, r2^2, r3^2, (r2*r3)^2, (r0*r3)^2, (r0*r2)^2, (r1*r3*r1*r2)^2, (r1*r3*r0*r1*r3)^2, (r2*r1*r2*r0*r1)^2, r1*r0*(r1*r2)^3*r1*r0*r1*r2, (r1*r0*r1*r3*r2*r1*r0)^2, (r2*r1*r3)^2*r0*r2*r1*r3*r2*r1*r0*r3, ((r1*r0)^3*r2)^2*(r1*r0)^3 ];;

• Number of Elements of each type

type 0: 9 elements

type 1: 81 elements

type 2: 6 elements

type 3: 6 elements

• Order of r₀ r₁ r₂ r₃ : 18

• This hypertope does not have non-degenerate leaves