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LuCo2 is Cubic Laves structured and crystallizes in the cubic Fd-3m space group. The structure is three-dimensional. Lu is bonded in a 12-coordinate geometry to twelve equivalent Co atoms. All Lu–Co bond lengths are 2.93 Å. Co is bonded to six equivalent Lu and six equivalent Co atoms to form a mixture of edge, face, and corner-sharing CoLu6Co6 cuboctahedra. All Co–Co bond lengths are 2.50 Å.
Lu2Co17 crystallizes in the hexagonal P6_3/mmc space group. The structure is three-dimensional. there are two inequivalent Lu sites. In the first Lu site, Lu is bonded in a 12-coordinate geometry to eighteen Co atoms. There are a spread of Lu–Co bond distances ranging from 2.90–3.23 Å. In the second Lu site, Lu is bonded in a 2-coordinate geometry to twenty Co atoms. There are a spread of Lu–Co bond distances ranging from 2.88–3.12 Å. There are four inequivalent Co sites. In the first Co site, Co is bonded in a 2-coordinate geometry to one Lu and thirteen Co atoms. There are a spread of Co–Co bond distances ranging from 2.31–2.67 Å. In the second Co site, Co is bonded to two equivalent Lu and ten Co atoms to form CoLu2Co10 cuboctahedra that share corners with fourteen CoLu2Co10 cuboctahedra, edges with six equivalent CoLu3Co9 cuboctahedra, and faces with ten CoLu2Co10 cuboctahedra. All Co–Co bond lengths are 2.39 Å. In the third Co site, Co is bonded in a 12-coordinate geometry to two Lu and ten Co atoms. There are a spread of Co–Co bond distances ranging from 2.33–2.51 Å. In the fourth Co site, Co is bonded to three Lu and nine Co atoms to form a mixture of distorted face, edge, and corner-sharing CoLu3Co9 cuboctahedra. Both Co–Co bond lengths are 2.40 Å.