Metals: crystals (or liquids) with unlocated electrons forming a cloud which may move easily in an electrical field.
Ceramics: may allow ion conduction, depending on the properties of the crystal lattice. The mechanism often involves ions moving into adjacent fault positions.
Polymers with a mesomeric conjugation along the entire molecule may conduct electricity. Graphite layers are an extreme example for this.
Melting points and hardness of ceramics and polymers may vary.
Ceramics are basically crystallites bonded across the edges via sintering (heating just below the melting point of the constituiting crystallites). This gives them two different "melting points" - the lower one for the bonds created by the sintering process, and another one for the crystallites.
Polymers rarely melt. Chain or layered polymers can soften when the vibration energy exceeds the van der Waals attractions or dipol attractions between the macromolecules.
Polymer hardness often will be anisotropic - soft along the polymer chains or layers, hard across the macromolecules.
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