Fracture theory predicts that polygonal cracks will form in the presence of an isotropic, extensional stress field. On Venus, polygonal fractures are observed on scales several orders of magnitude larger than on Earth, with an average diameter of 1.8 ¿ 0.9 km. Proposed formation mechanisms include cooling following lava flow emplacement, lithospheric heating, and climate change. Here we examine the characteristics and geologic setting of 204 regions of polygons. Some regions display two spatially overlapping size ranges, with the larger spacing typically 10--25 km. Most polygonal fractures appear to be extensional, but some have the morphology of compressional ridges. Polygons are confined to plains regions and occur in association with shield fields (49%), coronae and coronae-like features (21.3%), tessera (17.5%), and wrinkle ridges (20%). In locations where polygons occur with shield fields, coronae, or both, they appear to have formed contemporaneously. Formation in conjunction with local heating events is consistent with the lithospheric cooling hypothesis. However, there is almost never the predicted decrease in size away from the center of coronae or shield fields. Only a small percentage of coronae and shield fields contain polygons, indicating that they are not typical of the formation process. The climate change-induced scenario is consistent with many characteristics of the polygons, including the small and large size ranges, the compressional ridges, and their occurrence with and without evidence of local heating. Although polygons may have diverse origins, including formation by multiple deformation events, overall polygon characteristics support the climate change hypothesis.