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

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

• Structure of Group

S3 x D18 x S3

• Generators of Automorphism Group (Permutation Representation for GAP)

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

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

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

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

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