To deal with climate change, cities must reduce their greenhouse gas (GHG) emissions and at the same time mitigate climate impacts associated with the physical infrastructure of the built environment. One strand of literature demonstrates that compact cities of sufficient density result in lower GHG emissions in the transport and the buildings sectors compared to sprawled cities. Another strand of literature, however, reveals that compactness hinders climate adaptation by amplifying the urban heat island (UHI) effect. As a result, mitigation and adaptation objectives of cities appear to contradict each other. Here, we develop a geometrical optimization framework and model of a three-dimensional city that minimizes this conflict. It makes use of the observation that low-carbon efficient transport can be realized via linear public transport axes, and that GHG emissions and UHI effects scale differently with varying geometric properties, thus enabling design that reflects both the economics and the climate of cities. We find that star-shaped cities, in contrast to radially symmetric cities, are well suited to alleviate the problematic trade-off. We also demonstrate that urban design considerations depend on transport fuel prices. The results are of particular importance for city planners of rapidly urbanizing cities in Asia and Africa who still have the potential to shape urban layout.