Final answer:
The compound is likely an ionic solid based on its hard and rigid nature, the formation of similar three-dimensional shapes when broken, and its ability to conduct electricity when dissolved in water.
Step-by-step explanation:
The type of bonding in the compound can be predicted based on the given information. The fact that the solid is very hard and forms similar three-dimensional shapes when broken suggests that the particles are closely packed together in a rigid structure, indicating a crystalline solid. The fact that the compound conducts electricity when dissolved in water further suggests that it contains charged particles.
Based on these observations, the most likely type of bonding in this compound is ionic bonding. Ionic compounds are composed of positive and negative ions that are held together by electrostatic attractions. They have high melting points and are generally hard and rigid. They do not conduct electricity in the solid state due to their fixed structure, but they conduct well when molten or dissolved in water.