All analogies to God break down at some point because God is unique, but the best comparison I have heard is the triple point of a substance.
That is a good one. I also like C.S. Lewis' explanation in his book Mere Christianity:
The last chapter was about the difference between begetting and making. A man begets a child, but he only makes a statue. God begets Christ but He only makes men. But by saying that, I have illustrated only one point about God, namely, that what God the Father begets is God, something of the same kind as Himself. In that way it is like a human father begetting a human son. But not quite like it. So I must try to explain a little more.
A good many people nowadays say, "I believe in a God, but not in a personal God." They feel that the mysterious something which is behind all other things must be more than a person. Now the Christians quite agree. But the Christians are the only people who offer any idea of what a being that is beyond personality could be like. All the other people, though they say that God is beyond personality, really think of Him as something impersonal: that is, as something less than personal. If you are looking for something super-personal, something more than a person, then it is not a question of choosing between the Christian idea and the other ideas. The Christian idea is the only one on the market.
Again, some people think that after this life, or perhaps after several lives, human souls will be "absorbed" into God. But when they try to explain what they mean, they seem to be thinking of our being absorbed into God as one material thing is absorbed into another. They say it is like a drop of water slipping into the sea. But of course that is the end of the drop. If that is what happens to us, then being absorbed is the same as ceasing to exist. It is only the Christians who have any idea of how human souls can be taken into the life of God and yet remain themselves-in fact, be very much more themselves than they were before.
I warned you that Theology is practical. The whole purpose for which we exist is to be thus taken into the life of God. Wrong ideas about what that life is, will make it harder. And now, for a few minutes, I must ask you to follow rather carefully.
You know that in space you can move in three ways-to left or right, backwards or forwards, up or down. Every direction is either one of these three or a compromise between them. They are called the three Dimensions. Now notice this. If you are using only one dimension, you could draw only a straight line. If you are using two, you could draw a figure: say, a square. And a square is made up of four straight lines. Now a step further. If you have three dimensions, you can then build what we call a solid body, say, a cube-a thing like a dice or a lump of sugar. And a cube is made up of six squares.
Do you see the point? A world of one dimension would be a straight line. In a two-dimensional world, you still get straight lines, but many lines make one figure. In a three-dimensional world, you still get figures but many figures make one solid body. In other words, as you advance to more real and more complicated levels, you do not leave behind you the things you found on the simpler levels: you still have them, but combined in new ways-in ways you could not imagine if you knew only the simpler levels.
Now the Christian account of God involves just the same principle. The human level is a simple and rather empty level. On the human level one person is one being, and any two persons are two separate beings-just as, in two dimensions (say on a flat sheet of paper) one square is one figure, and any two squares are two separate figures. On the Divine level you still find personalities; but up there you find them combined in new ways which we, who do not live on that level, cannot imagine. In God's dimension, so to speak, you find a being who is three Persons while remaining one Being, just as a cube is six squares while remaining one cube. Of course we cannot fully conceive a Being like that: just as, if we were so made that we perceived only two dimensions in space we could never properly imagine a cube. But we can get a sort of faint notion of it. And when we do, we are then, for the first time in our lives, getting some positive idea, however faint, of something super-personal-something more than a person. It is something we could never have guessed, and yet, once we have been told, one almost feels one ought to have been able to guess it because it fits in so well with all the things we know already.
You may ask, "If we cannot imagine a three-personal Being, what is the good of talking about Him?" Well, there isn't any good talking about Him. The thing that matters is being actually drawn into that three-personal life, and that may begin any time -tonight, if you like.
What I mean is this. An ordinary simple Christian kneels down to say his prayers. He is trying to get into touch with God. But if he is a Christian he knows that what is prompting him to pray is also God: God, so to speak, inside him. But he also knows that all his real knowledge of God comes through Christ, the Man who was God-that Christ is standing beside him, helping him to pray, praying for him. You see what is happening. God is the thing to which he is praying-the goal he is trying to reach. God is also the thing inside him which is pushing him on-the motive power. God is also the road or bridge along which he is being pushed to that goal. So that the whole threefold life of the three-personal Being is actually going on in that ordinary little bedroom where an ordinary man is saying his prayers. The man is being caught up into the higher kind of life-what I called Zoe or spiritual life: he is being pulled into God, by God, while still remaining himself.
http://www.truthaccordingtoscripture.com/documents/apologetics/mere-christianity/Book4/cs-lewis-mere-christianity-book4.php#b
