This paper focuses on the dynamics of the eight tridimensional principal
slices of the tricomplex Mandelbrot set for the power 2: 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
M3, we show that one of them corresponds to a third Platonic
solid: the cube
