Rank 4 Tail-triangle diagram with parameters (a,b,c,d) = (6,6,3,6)

Small Group ID = [648,732], hypertope number 2.

• Structure of Group

S3 x S3 x ((C3 x C3) : C2)

• Generators of Automorphism Group (Permutation Representation for GAP)

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

r1 := (2,5)(3,8)(4,9)(6,14)(7,16)(10,21)(11,22)(12,17)(13,24)(15,27)(18,28)(19,26)(20,31)(23,25)(29,30)(33,34);

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

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

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

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

• Number of Elements of each type

type 0: 6 elements

type 1: 27 elements

type 2: 18 elements

type 3: 9 elements

• Order of r₀ r₁ r₂ r₃ : 6

• This hypertope does not have non-degenerate leaves