Logical contradictions and the trinity

This question may seem strange, but I believe it is valid. It is commonly understood that God cannot create logical contradictions, such as a square circle, or make 1+1=3. However, it seems that the trinity itself is a logical contradiction being three distinct persons but still only one God. Why can God not create logical contradictions when his own nature is a logical contradiction? I am a trinitarian, but I am unsure of how to answer this question.