peeters parent
It's a meaningless distinction. A solid is defined by a 3D shape enclosed by a surface. It doesn't require uniform density. Just imagine that the sides of this surface are infinitesimally thin so as to be invisible and porous to air, and you've filled the definition. Don't like this answer, then just imagine the same thing but with an actual thin shell like mylar. It makes no difference.
Oops disregard this, by "has to be identical" I thought you were objecting to the non uniformity of the surface, not the incongruity of the sides' shapes, so that's where my comment was coming from.
The incongruity of the sides certainly makes it not a Platonic Solid, though the article doesn't actually assert that it is. It just uses some terrible phrasing that's bound to mislead. Their words with my clarification for how it could be parsed in a factually accurate way: "A tetrahedron is the simplest Platonic solid (when it's a regular tetrahedron). Mathematicians have now made one (a tetrahedron, not a Platonic solid)...".
It's a dumb phrasing, it's like saying "Tesla makes the world's fastest accelerating sports car. I bought one" and then revealing that the "one" refers to a Tesla Model 3, not the fastest accelerating sports car.