  This paper focuses on the dynamics of the eight tridimensional principal
slices of the tricomplex Mandelbrot set: the Tetrabrot, the Arrowheadbrot, the
Mousebrot, the Turtlebrot, the Hourglassbrot, the Metabrot, the Airbrot
(octahedron) and the Firebrot (tetrahedron). In particular, we establish a
geometrical classification of these 3D slices using the properties of some
specific sets that correspond to projections of the bicomplex Mandelbrot set on
various two-dimensional vector subspaces, and we prove that the Firebrot is a
regular tetrahedron. Finally, we construct the so-called "Stella octangula" as
a tricomplex dynamical system composed of the union of the Firebrot and its
dual, and after defining the idempotent 3D slices of $\mathcal{M}_{3}$, we show
that one of them corresponds to a third Platonic solid: the cube.

Dynamical Systems