Crystallography indicates that the structure of the atomic nucleus must follow a crystal-like order. Quasicrystals and Atomic Clusters with a precise Icosahedral- and Dodecahedral structure indicate that the five Platonic Solids are the theoretical framework behind the design of the atomic nucleus. With my study I advance the hypothesis that the reference for the shell-structure of the atomic nucleus are the Platonic Solids. In my new model of the atomic nucleus I consider the central space diagonals of the Platonic Solids as the long axes of Proton- or Neutron Orbitals, which are similar to electron orbitals. Ten such Proton- or Neutron Orbitals form a complete dodecahedral orbital-structure (shell), which is the shell-type with the maximum number of protons or neutrons. An atomic nucleus therefore mainly consists of dodecahedral shaped shells. But stable Icosahedral- and Hexagonal-(cubic) shells also appear in certain elements. Constant Phi which directly appears in the geometry of the Dodecahedron and Icosahedron seems to be the fundamental constant that defines the structure of the atomic nucleus and the structure of the wave systems (orbitals) which form the atomic nucelus. Albert Einstein wrote in a letter that the true constants of an Universal Theory must be mathematical constants like Pi (π) or e. My mathematical discovery described in chapter 5 shows that all irrational square roots of the natural numbers and even constant Pi (π) can be expressed with algebraic terms which only contain constant Phi (ϕ) and 1. Therefore it is logical to assume that constant Phi, which also defines the structure of the Platonic Solids must be the fundamental constant that defines the structure of the atomic nucleus. Indication for the important role which the Dodecahedron plays in the structure of a matter also seems to come from the observation of the M87 black hole.