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Three-dimensional genome structures play a key role in gene regulation and cell functions. Characterization of genome structures necessitates single-cell measurements. This has been achieved for haploid cells but has remained a challenge for diploid cells. We developed a single-cell chromatin conformation capture method, termed Dip-C, that combines a transposon-based whole-genome amplification method to detect many chromatin contacts, called META (multiplex end-tagging amplification), and an algorithm to impute the two chromosome haplotypes linked by each contact. We reconstructed the genome structures of single diploid human cells from a lymphoblastoid cell line and from primary blood cells with high spatial resolution, locating specific single-nucleotide and copy number variations in the nucleus. The two alleles of imprinted loci and the two X chromosomes were structurally different. Cells of different types displayed statistically distinct genome structures. Such structural cell typing is crucial for understanding cell functions.