Polyploidy, increased sets of chromosomes, occurs during development, cellular stress, disease and evolution. Despite its prevalence, little is known about the physiological alterations that accompany polyploidy. We previously described 'ploidy-specific lethality', where a gene deletion that is not lethal in haploid or diploid budding yeast causes lethality in triploids or tetraploids. Here we report a genome-wide screen to identify ploidy-specific lethal functions. Only 39 out of 3,740 mutations screened exhibited ploidy-specific lethality. Almost all of these mutations affect genomic stability by impairing homologous recombination, sister chromatid cohesion, or mitotic spindle function. We uncovered defects in wild-type tetraploids predicted by the screen, and identified mechanisms by which tetraploidization affects genomic stability. We show that tetraploids have a high incidence of syntelic/monopolar kinetochore attachments to the spindle pole. We suggest that this defect can be explained by mismatches in the ability to scale the size of the spindle pole body, spindle and kinetochores. Thus, geometric constraints may have profound effects on genome stability; the phenomenon described here may be relevant in a variety of biological contexts, including disease states such as cancer.