Sex chromosome aneuploidies (SCAs) are common genetic syndromes characterized by the presence of an aberrant number of X and Y chromosomes due to meiotic defects. These conditions impact the structure and function of diverse tissues, but the proximal effects of SCAs on genome organization are unknown. Here, to determine the consequences of SCAs on global genome organization, we have analyzed multiple architectural features of chromosome organization in a comprehensive set of primary cells from SCA patients with various ratios of X and Y chromosomes by use of imaging-based high-throughput chromosome territory mapping (HiCTMap). We find that X chromosome supernumeracy does not affect the size, volume, or nuclear position of the Y chromosome or an autosomal chromosome. In contrast, the active X chromosome undergoes architectural changes as a function of increasing X copy number as measured by a decrease in size and an increase in circularity, which is indicative of chromatin compaction. In Y chromosome supernumeracy, Y chromosome size is reduced suggesting higher chromatin condensation. The radial positioning of chromosomes is unaffected in SCA karyotypes. Taken together, these observations document changes in genome architecture in response to alterations in sex chromosome numbers and point to trans-effects of dosage compensation on chromosome organization.