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

Small Group ID = [648,732], hypertope number 1.

• Structure of Group

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

• Generators of Automorphism Group (Permutation Representation for GAP)

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

r1 := (2,5)(3,8)(4,9)(6,14)(7,16)(10,21)(11,22)(12,15)(13,24)(17,26)(18,30)(19,27)(20,32)(23,28)(25,34)(31,35);

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

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

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

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

• 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