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

Small Group ID = [648,554], hypertope number 3.

• Structure of Group

D18 x S3 x S3

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (1,2)(3,6)(4,7)(5,11)(8,14)(9,15)(10,20)(12,23)(13,24)(16,30)(17,27)(18,28)(19,29)(21,35)(22,26)(25,36)(31,33)(32,34);

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

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

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

• 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*(r0*r1)^2)^2, (r2*(r1*r0)^2*r1)^2, (r1*r0)^6, (r0*r1*r2*r3*r0*r1*r2)^2, r2*(r1*r3)^2*r2*r1*r0*(r1*r3*r2)^2*r1*r0, (r1*r0*r1*r3*r2*r1*r3*r0*r2*r1*r3)^2, ((r1*r3*r2)^2*r1*r3)^3 ];;

• Number of Elements of each type

type 0: 6 elements

type 1: 81 elements

type 2: 6 elements

type 3: 9 elements

• Order of r₀ r₁ r₂ r₃ : 18

• This hypertope does not have non-degenerate leaves