The silver medal trinity?

I very much enjoyed watching the Olympic Games. Last weekend I saw a picture in the newspaper of the Australian men’s cycling team pursuit team wearing their silver medals. As I saw this picture it struck me that this might be a way of understanding God. How could this be?
Christians understand God as a Trinity, i.e. three distinct persons all sharing the same ‘God’ essence. Many struggle to comprehend the Trinity, but I wonder if the Olympic medal ceremony could help us?
When the Olympic cycling pursuit team stand up on the podium there are four athletes receiving medals – there are four individual medallists. Yet only one medal has been added to the medal tally. For these cyclists, it seems that they have earned only ‘one’ silver medal despite the fact that there have been four medals awarded. Each of the medallists are individual and distinct, yet they also share in the same ‘one’ silver medal.
This is similar in many ways with the Trinity. The Bible makes it very clear that God is one. Yet Jesus speaks and acts as God and he also speaks of the Father as being different to him. The way we understand this perceived mystery is similar to the medal tally. God is one, but also three distinct persons (the Father, Son and Spirit) – God is ‘three-in-one’. This ‘three-in-one’ nature of God is similar to the ‘four-in-one’ nature of the medal tally.
Does this help us understand the nature of God? Would be keen to hear your thoughts.