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

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

• Structure of Group

S3 x D18 x S3

• Generators of Automorphism Group (Permutation Representation for GAP)

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

r1 := (2,5)(3,8)(4,10)(6,14)(9,19)(11,22)(12,25)(13,20)(15,29)(16,30)(17,31)(18,32)(21,36)(23,27)(26,28)(33,34);

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

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

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

G := F/[ r2^2, r0^2, r1^2, r3^2, (r3*r2)^2, (r0*r3)^2, (r0*r2)^2, (r1*r2*r3*r0*r1*r3)^2, r1*r2*r0*r3*r1*r0*r1*r2*r3*r0*r1*r0, ((r1*r2)^2*r0*r1*r0)^2, (r2*(r0*r1*r3)^2)^2, (r3*r1*r0)^6, r2*r3*r0*r1*r0*r2*r3*(r1*r2)^3*r3*r0*r1*r2*r1*r0*r3*r2*r1*r3*r2*r3*r1*r2*r1 ];;

• Number of Elements of each type

type 0: 6 elements

type 1: 81 elements

type 2: 9 elements

type 3: 6 elements

• Order of r₀ r₁ r₂ r₃ : 18

• This hypertope does not have non-degenerate leaves