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In gemology it seems to be called a hexoctahedron. This is a specific shape in which it is as if each face of a cube has a square based pyramid attached, covering its square face. There are others and from Greek it could be called an eicosakaitesserahedron. At least that's how the shapes are usually named!

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Q: What is the name of a 3d shape with 24 faces?
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