Many sets of ethics principles for responsible AI have been proposed to allay concerns about misuse and abuse of AI/ML systems. The underlying aspects of such sets of principles include privacy, accuracy, fairness, robustness, explainability, and transparency. However, there are potential tensions between these aspects that pose difficulties for AI/ML developers seeking to follow these principles. For example, increasing the accuracy of an AI/ML system may reduce its explainability. As part of the ongoing effort to operationalise the principles into practice, in this work we compile and discuss a catalogue of 10 notable tensions, trade-offs and other interactions between the underlying aspects. We primarily focus on two-sided interactions, drawing on support spread across a diverse literature. This catalogue can be helpful in raising awareness of the possible interactions between aspects of ethics principles, as well as facilitating well-supported judgements by the designers and developers of AI/ML systems.