  Multiple line nodes in energy-band gaps are found in semimetals preserving
mirror-reflection symmetry. We classify possible configurations of multiple
line nodes with crossing points (crossing line nodes) under point-group
symmetry. Taking the spin-orbit interaction (SOI) into account, we also
classify topological phase transitions from crossing-line-node Dirac semimetals
to other topological phases, e.g., topological insulators and point-node
semimetals. This study enables one to find crossing-line-node semimetal
materials and their behavior in the presence of SOI from the band structure in
the absence of SOI without detailed calculations. As an example, the theory
applies to hexagonal rare-earth trihydrides with the HoD3 structure and
clarifies that it is a crossing-line-node Dirac semimetal hosting three line
nodes.
