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

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

• Structure of Group

S3 x S3 x D18

• Generators of Automorphism Group (Permutation Representation for GAP)

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

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

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

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

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

G := F/[ r3^2, r0^2, r1^2, r2^2, (r2*r0)^2, (r2*r3)^2, (r0*r3)^2, (r1*r2*r1*r0)^2, (r0*r3*r1*r0*r1)^2, (r1*r3*r1*r2)^2*r1*r2*r1*r2, (r0*r3*r1*r0*r2*r1*r2)^2, (r2*r1*r0)^6, r3*r1*((r3*r1)^2*r0)^2*r3*r1*r3*(r1*r3*r0)^2*r1 ];;

• 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