Answer:
Everyday symbols for the Trinity are usually avoided in Christianity because God's existence in a Triune state is so radically different from the way we exist as humans. Anything that could be used as a symbol of Trinity - for example the three phases of water, existing as water, steam and ice but yet always remaining water in the chemical sense - usually degrades into some form of heresy or degrades our concept of the Trinity to such a degree that it may be considered idol worship. This example, for instance, is Modalism, a heresy.
There is also a very traditional chart used in many churches (even from the Middle Ages) that tries to depict what the Trinity is like. It is often called "the shield of the Holy Trinity" or something to that effect. This, at least, is generally accepted by theologians, and does not lead into the heart of tritheistic and modalistic heresies like the popular clover (three leaves), egg (three parts), or water (three phases) images.