The three-dimensional (3D) folding of the chromosomal fibre in the human interphase nucleus is an important, but poorly understood aspect of gene regulation. Especially basic principles of 3D chromatin and chromosome organisation are still elusive. In this paper, we quantitatively analyse the 3D structure of large parts of chromosomes 1 and 11 in the G1 nucleus of human cells and relate it to the human transcriptome map (HTM). Despite a considerable cell-to-cell variation, our results show that subchromosomal domains, which are highly expressed, are more decondensed, have a more irregular shape and are located in the nuclear interior compared to clusters of low expressed genes. These aspects of chromosome structure are shared by six different cell lines and therefore are independent of cell type specific differences in gene expression within the investigated domains. Systematic measurements show that there is little to no intermingling of chromatin from different parts of the same chromosome, indicating that the chromosomal fibre itself is a compact structure. Together, our results reveal several basic aspects of 3D chromosome architecture, which are related to genome function.