How to generate tetrahedron from a mesh?

[zhang-qiang-github]

Is it possible to generate tetrahedron from a mesh?

The mesh means points and the connection. For a 3D cubic, it look likes:

points = [
    [0, 0, 0],
    [1, 0, 0], 
    [1, 1, 0], 
    [0, 1, 0], 
    [0, 0, 1],
    [1, 0, 1], 
    [1, 1, 1], 
    [0, 1, 1], 
]
connection = [
    [0, 1, 2, 3],
    [4, 5, 6, 7],
    [0, 1, 5, 4],
    [1, 2, 6, 5],
    [2, 3, 7, 6],
    [0, 3, 7, 4],
]

Can I generate the tetrahedron from this cubic?

In addition, for the generated tetrahedron, does it would generate new point in the cubic surface? For example, generate a point 0.5, 0.5, 0. If it generate new point in the surface, how can I obtain the mesh of new surface?

Any suggestion is appreciated~~~