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How to create Polyhedra .obj Animation?

Hi Everyone! The best way to explain what I am trying to do is to show you a gif, so hers a link to a Wikipedia page: File:Small stellated dodecahedron truncations.gif - Wikipedia

So what I need is to make that type of animation in 3D…to be used as “a pick up” object or as the skeletal mesh/ avatar for a player or enemy…

Now to create a static polyhedra .obj is easy, many different options, programs, websites to export polyhedra in .obj format.

One simple thing I have done is just to take two objects, such as two cubes, put them in the SAME SPACE and add a rotation to one or both and you get exactly the type of effect I am looking for, fluctuating, animated, flowing, polyhedra… but only in a superficial way…nothing like a true real time flowing sequence of polyhedra variables.

The ultimate thing for me would be to be able to have a polyhedra object in game with variables so that the transition from one polyhedra form to the next and back…could be changed, over time, or based on how many hits it takes, or many other things that might change the value of that variable and therefore change the shape of the polyhedra…BUT I would settle for at least a “static/repeating animated transition/flow” that just repeats just like in the gif but a 3D object.

If anyone can tell me what PROGRAMS I might use for this…or a BASIC workflow idea, please help!