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

Small Group ID = [648,554], hypertope number 1.

• 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)(10,20)(11,22)(14,25)(15,24)(16,28)(18,31)(19,32)(21,35)(23,36)(26,30)(27,29)(33,34);

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

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

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

• 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, ((r3*r1)^2*r0)^2, (r2*r1*r2*r0*r1)^2, (r0*r1*r3*r1*r0*r1)^2, r2*r1*r0*r1*r3*r1*r2*r1*r3*r1*r0*r1, (r3*r1*r3*r0*r2*r1*r2)^2, r1*r3*r0*r1*r0*r2*r1*r0*r1*r2*r3*r0*r1*r3*r0*r2*r1*r2*(r0*r1*r3)^3*r0 ];;

• 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