In traditional astronomies across the world, groups of stars in the night sky were linked into constellations -- symbolic representations rich in meaning and with practical roles. In some sky cultures, constellations are represented as line (or connect-the-dot) figures, which are spatial networks drawn over the fixed background of stars. We analyse 1802 line figures from 56 sky cultures spanning all continents, in terms of their network, spatial, and brightness features, and ask what associations exist between these visual features and culture type or sky region. First, an embedded map of constellations is learnt, to show clusters of line figures. We then form the network of constellations (as linked by their similarity), to study how similar cultures are by computing their assortativity (or homophily) over the network. Finally, we measure the diversity (or entropy) index for the set of constellations drawn per sky region. Our results show distinct types of line figures, and that many folk astronomies with oral traditions have widespread similarities in constellation design, which do not align with cultural ancestry. In a minority of sky regions, certain line designs appear universal, but this is not the norm: in the majority of sky regions, the line geometries are diverse.