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

Small Group ID = [256,16888], hypertope number 2.

• Structure of Group

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

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (1,2)(3,5)(4,7)(6,10)(8,13)(9,12)(11,14)(15,16);

r1 := (1,3)(2,4)(5,9)(6,11)(7,12)(8,14)(10,15)(13,16);

r2 := (3,6)(4,8)(5,10)(7,13);

r3 := (3,4)(5,7)(11,14)(15,16);

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

G := F/[ r3^2, r2^2, r0^2, r1^2, (r0*r3)^2, (r0*r2)^2, (r1*r3)^4, (r1*r2)^4, (r1*r0*r1*r2)^2, (r1*r2*r3*r2)^2, (r2*r3)^4, (r1*r3*r1*r0)^2, (r0*r1)^4, (r1*r3*r1*r2*r3)^2 ];;

• Number of Elements of each type

type 0: 4 elements

type 1: 16 elements

type 2: 8 elements

type 3: 8 elements

• Order of r₀ r₁ r₂ r₃ : 4

• This hypertope does not have non-degenerate leaves