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

Small Group ID = [288,1036], hypertope number 1.

• Structure of Group

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

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (1,2)(3,6)(4,7)(5,11)(8,15)(9,19)(10,16)(12,14)(13,22)(17,18)(20,23)(21,24);

r1 := (1,3)(2,5)(4,9)(6,14)(7,10)(8,17)(11,12)(13,21)(15,24)(16,20)(18,22)(19,23);

r2 := (1,3)(2,6)(4,10)(5,12)(7,16)(8,18)(9,20)(11,14)(13,21)(15,17)(19,23)(22,24);

r3 := (1,4)(2,7)(3,8)(5,13)(6,15)(9,17)(10,21)(11,22)(12,23)(14,20)(16,24)(18,19);

• 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, (r0*r3)^2, (r0*r2)^2, (r1*r3)^3, (r2*r1)^3, (r3*r0*r2*r1*r3*r2*r1)^2, r3*r1*r2*r0*r3*r2*r1*r0*r3*r1*r3*r2*r0*r3*r2, r1*r3*r2*r3*r1*r2*r1*(r0*r3*r2)^2*r3*r2*r3 ];;

• Number of Elements of each type

type 0: 4 elements

type 1: 12 elements

type 2: 12 elements

type 3: 12 elements

• Order of r₀ r₁ r₂ r₃ : 4

• This hypertope does not have non-degenerate leaves