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Q: What solids have no faces?

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Platonic solids are regular polyhedra whose faces are all regular polygons, such that the same number of faces meet at each vertex.The five Platonic solids areTetrahedron - 4 triangular faces;Cube - 6 square faces;Octahedron - 8 triangular faces;Dodecahedron - 12 pentagonal faces;Icosahedron - 20 triangular faces.

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A circle

You probably mean the Platonic Solids, they are the only five shapes constructed from the same faces.

The five platonic solids.

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