Polyhedral Stelations: These are the processes of geometric transformations through which a face, several faces or all the faces of a selected polyhedron are modified, to form a new polyhedron.
<p>According to the application of the geometric transformations in each of the faces of a selected polyhedron, the polyhedral stelations are classified into two types, which are: uniform polyhedral stelations and deformed polyhedral stelations. Deformed polyhedral stelations are classified into two types which are: Total deformed polyhedral stelations and partial deformed polyhedral stelations.
Uniform polyhedral stelations according to the degree of perfection are classified as: Perfect uniform polyhedral stelations and imperfect uniform polyhedral stelations. Perfect uniform polyhedral stelations are called by the name of regular uniform polyhedral stelations and imperfect uniform polyhedral stelations are called by the name of irregular uniform polyhedral stelations. All deformed polyhedral stelations are imperfect or irregular.
 
a) Uniform polyhedral stelations: they are those through which, the geometric transformations are applied in the same way on all the faces of a selected polyhedron, until a new polyhedron is formed.
b) Perfect or regular polyhedral stelations: they are stellations where the set of vertices is uniform, the set of edges is uniform and the set of all its faces are regular uniform faces.
c) Imperfect or irregular polyhedral stelations: they are stellations where the set of vertices is non-uniform, or the set of edges is non-uniform and the set of all its faces are non-uniform faces or irregular faces.
d) Total deformed polyhedral stelations: They are the one where geometric transformations are applied in different ways on all the faces of a selected polyhedron, until a new polyhedron is formed.
e) Partial deformed polyhedral stelations: They are those where geometric transformations are applied differently on a face, or on several of those of the faces of a selected polyhedron, until a new polyhedron is formed.
Polyhedral stellations according to the position of their faces are classified as: Convex polyhedral stelations, concave polyhedral stelations.
Convex stelations are sub-divided into simple stelations and compound stelations.
Concave stellations are classified into three basic classes which are: Starry stelae, hollow stellations, mixed stellations.
Uniform tetrahedron stelation: It is the process by which the faces of the tetrahedron are extended symmetrically until they all meet again, forming a new stellated polyhedron.
According to the new theory of polyhedral stelations of Professor Jose Joel Leonardo:
1) All polyhedra have an infinite amount of hollow stelations, this is because the space is infinitely divisible.
2) The tetrahedron has nine (9) essential stelations.
3) The hexahedron or cube has nine (9) fundamental stelations.
4) The octahedron has eight (8) main stelations.
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5) The dodecahedron has nine (9) elementary stelations.
<a href="//commons.wikimedia.org/wiki/User:Jose_J._Leonard" title="User:Jose J. Leonard">Jose J. Leonard</a>
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