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

Small Group ID = [192,1490], hypertope number 1.

• Structure of Group

((C2 x C2 x Q8) : C3) : C2

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (1,2)(3,5)(4,6)(8,10)(14,16)(19,22)(20,21)(23,24);

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

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

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

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

G := F/[ r0^2, r3^2, r1^2, r2^2, (r2*r0)^2, (r0*r3)^2, (r1*r2)^3, (r1*r3)^3, (r3*r2)^4, (r1*r3*r0)^3, (r1*r2*r0)^3, r2*r3*r1*r0*r2*r1*r3*r2*r1*r0*r3*r1 ];;

• Number of Elements of each type

type 0: 4 elements

type 1: 12 elements

type 2: 8 elements

type 3: 8 elements

• Order of r₀ r₁ r₂ r₃ : 8

• This hypertope does not have non-degenerate leaves