Short answer

No. The example says one thing, water, can be ice, liquid and steam. So, they say, the Trinitarian God can be Father, Son and Holy Spirit. But water becomes ice or steam by turns, as it cools or heats. That pictures one being taking three forms at different times. The early Church condemned exactly that teaching as a heresy, called modalism. At one exact point, called the triple point, water can be all three at once. But then there are three portions of water, and each is only part of it. That makes each person only a part of God, and the creeds deny that too. If instead each portion is a whole water, there are three waters, and so three Gods. Other pictures, such as the egg, the shamrock and the sun, fail in the same ways. The Qur'an says: "Invent not similitudes for Allah". God (﷾) is One, and there is none like Him.

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