This paper focuses on roof-shape classification and solar potential for integrating photovoltaics (PV) on roofs. A machine-learning approach, Support Vector Machine (SVM), is used to classify the roof shapes in the city of Geneva. The impact of various roof characteristics on the solar potential is assessed and analyzed. Monthly solar irradiation on rooftops, freely accessible from www.ge.ch/sitg using GIS LiDAR data (resolution 50cm by 50cm), is used in the analysis. The SVM identifies 6 types of roof shapes correctly in 66% of cases, that is, flat, gable, hip, gambrel & mansard, cross/corner gable & hip, and complex roof. We rank the roofs based on the complexity of their shape, useful area for PV, and potential for receiving solar energy. The results show that for most roof shapes the ratio between useful roof areas and building footprint area is close to one, the main exception being gable where the ratio is 1.18, suggesting that footprint is a good measure of useful PV roof area. The flat roof has the second highest useful roof area for PV (complex roof being the highest) and the highest PV potential (in GWh). By contrast, hip roof has the lowest PV potential. Solar roof-shape classification provides basic information for designing new buildings, retrofitting interventions on the building roofs and efficient solar integration on rooftops. The results for the city of Geneva suggest that data-driven approach is very useful for roof-shape classification which can be expanded to the national scale.