HoAl3 crystallizes in the trigonal R-3m space group. There are three inequivalent Ho sites. In the first Ho site, Ho(1) is bonded to three equivalent Al(2), three equivalent Al(3), and six equivalent Al(1) atoms to form HoAl12 cuboctahedra that share corners with three equivalent Ho(2)Al12 cuboctahedra, corners with nine equivalent Ho(1)Al12 cuboctahedra, edges with six equivalent Al(2)Ho4Al8 cuboctahedra, edges with nine equivalent Al(3)Ho4Al8 cuboctahedra, faces with three equivalent Ho(2)Al12 cuboctahedra, faces with three equivalent Ho(3)Al12 cuboctahedra, faces with three equivalent Al(2)Ho4Al8 cuboctahedra, and faces with three equivalent Al(3)Ho4Al8 cuboctahedra. In the second Ho site, Ho(2) is bonded to three equivalent Al(1) and nine equivalent Al(3) atoms to form HoAl12 cuboctahedra that share corners with three equivalent Ho(1)Al12 cuboctahedra, corners with six equivalent Ho(2)Al12 cuboctahedra, corners with six equivalent Al(2)Ho4Al8 cuboctahedra, edges with twelve equivalent Al(3)Ho4Al8 cuboctahedra,  a faceface with one Ho(3)Al12 cuboctahedra, faces with three equivalent Ho(1)Al12 cuboctahedra, faces with three equivalent Ho(2)Al12 cuboctahedra, and faces with nine equivalent Al(3)Ho4Al8 cuboctahedra. In the third Ho site, Ho(3) is bonded to six equivalent Al(1) and six equivalent Al(2) atoms to form HoAl12 cuboctahedra that share corners with six equivalent Ho(3)Al12 cuboctahedra, corners with twelve equivalent Al(3)Ho4Al8 cuboctahedra, edges with six equivalent Al(2)Ho4Al8 cuboctahedra, faces with two equivalent Ho(2)Al12 cuboctahedra, faces with six equivalent Ho(1)Al12 cuboctahedra, and faces with six equivalent Al(2)Ho4Al8 cuboctahedra. There are three inequivalent Al sites. In the first Al site, Al(1) is bonded in a 10-coordinate geometry to one Ho(2), one Ho(3), two equivalent Ho(1), two equivalent Al(1), two equivalent Al(2), and two equivalent Al(3) atoms. In the second Al site, Al(2) is bonded to two equivalent Ho(1), two equivalent Ho(3), four equivalent Al(1), and four equivalent Al(2) atoms to form distorted AlHo4Al8 cuboctahedra that share corners with four equivalent Ho(2)Al12 cuboctahedra, corners with six equivalent Al(2)Ho4Al8 cuboctahedra, corners with eight equivalent Al(3)Ho4Al8 cuboctahedra, edges with two equivalent Ho(3)Al12 cuboctahedra, edges with four equivalent Ho(1)Al12 cuboctahedra, edges with four equivalent Al(2)Ho4Al8 cuboctahedra, faces with two equivalent Ho(1)Al12 cuboctahedra, faces with two equivalent Ho(3)Al12 cuboctahedra, faces with two equivalent Al(3)Ho4Al8 cuboctahedra, and faces with four equivalent Al(2)Ho4Al8 cuboctahedra. In the third Al site, Al(3) is bonded to one Ho(1), three equivalent Ho(2), two equivalent Al(1), and six equivalent Al(3) atoms to form distorted AlHo4Al8 cuboctahedra that share corners with two equivalent Ho(3)Al12 cuboctahedra, corners with four equivalent Al(2)Ho4Al8 cuboctahedra, corners with six equivalent Al(3)Ho4Al8 cuboctahedra, edges with three equivalent Ho(1)Al12 cuboctahedra, edges with four equivalent Ho(2)Al12 cuboctahedra, edges with eight equivalent Al(3)Ho4Al8 cuboctahedra,  a faceface with one Ho(1)Al12 cuboctahedra,  a faceface with one Al(2)Ho4Al8 cuboctahedra, faces with three equivalent Ho(2)Al12 cuboctahedra, and faces with nine equivalent Al(3)Ho4Al8 cuboctahedra.
HoAl3 crystallizes in the trigonal R-3m space group. There are three inequivalent Ho sites. In the first Ho site, Ho(1) is bonded to three equivalent Al(2), three equivalent Al(3), and six equivalent Al(1) atoms to form HoAl12 cuboctahedra that share corners with three equivalent Ho(2)Al12 cuboctahedra, corners with nine equivalent Ho(1)Al12 cuboctahedra, edges with six equivalent Al(2)Ho4Al8 cuboctahedra, edges with nine equivalent Al(3)Ho4Al8 cuboctahedra, faces with three equivalent Ho(2)Al12 cuboctahedra, faces with three equivalent Ho(3)Al12 cuboctahedra, faces with three equivalent Al(2)Ho4Al8 cuboctahedra, and faces with three equivalent Al(3)Ho4Al8 cuboctahedra. All Ho(1)-Al(2) bond lengths are 2.95 Å. All Ho(1)-Al(3) bond lengths are 2.97 Å. All Ho(1)-Al(1) bond lengths are 3.03 Å. In the second Ho site, Ho(2) is bonded to three equivalent Al(1) and nine equivalent Al(3) atoms to form HoAl12 cuboctahedra that share corners with three equivalent Ho(1)Al12 cuboctahedra, corners with six equivalent Ho(2)Al12 cuboctahedra, corners with six equivalent Al(2)Ho4Al8 cuboctahedra, edges with twelve equivalent Al(3)Ho4Al8 cuboctahedra,  a faceface with one Ho(3)Al12 cuboctahedra, faces with three equivalent Ho(1)Al12 cuboctahedra, faces with three equivalent Ho(2)Al12 cuboctahedra, and faces with nine equivalent Al(3)Ho4Al8 cuboctahedra. All Ho(2)-Al(1) bond lengths are 3.01 Å. There are three shorter (2.99 Å) and six longer (3.03 Å) Ho(2)-Al(3) bond lengths. In the third Ho site, Ho(3) is bonded to six equivalent Al(1) and six equivalent Al(2) atoms to form HoAl12 cuboctahedra that share corners with six equivalent Ho(3)Al12 cuboctahedra, corners with twelve equivalent Al(3)Ho4Al8 cuboctahedra, edges with six equivalent Al(2)Ho4Al8 cuboctahedra, faces with two equivalent Ho(2)Al12 cuboctahedra, faces with six equivalent Ho(1)Al12 cuboctahedra, and faces with six equivalent Al(2)Ho4Al8 cuboctahedra. All Ho(3)-Al(1) bond lengths are 3.05 Å. All Ho(3)-Al(2) bond lengths are 3.03 Å. There are three inequivalent Al sites. In the first Al site, Al(1) is bonded in a 10-coordinate geometry to one Ho(2), one Ho(3), two equivalent Ho(1), two equivalent Al(1), two equivalent Al(2), and two equivalent Al(3) atoms. Both Al(1)-Al(1) bond lengths are 2.71 Å. Both Al(1)-Al(2) bond lengths are 2.89 Å. Both Al(1)-Al(3) bond lengths are 2.91 Å. In the second Al site, Al(2) is bonded to two equivalent Ho(1), two equivalent Ho(3), four equivalent Al(1), and four equivalent Al(2) atoms to form distorted AlHo4Al8 cuboctahedra that share corners with four equivalent Ho(2)Al12 cuboctahedra, corners with six equivalent Al(2)Ho4Al8 cuboctahedra, corners with eight equivalent Al(3)Ho4Al8 cuboctahedra, edges with two equivalent Ho(3)Al12 cuboctahedra, edges with four equivalent Ho(1)Al12 cuboctahedra, edges with four equivalent Al(2)Ho4Al8 cuboctahedra, faces with two equivalent Ho(1)Al12 cuboctahedra, faces with two equivalent Ho(3)Al12 cuboctahedra, faces with two equivalent Al(3)Ho4Al8 cuboctahedra, and faces with four equivalent Al(2)Ho4Al8 cuboctahedra. All Al(2)-Al(2) bond lengths are 3.03 Å. In the third Al site, Al(3) is bonded to one Ho(1), three equivalent Ho(2), two equivalent Al(1), and six equivalent Al(3) atoms to form distorted AlHo4Al8 cuboctahedra that share corners with two equivalent Ho(3)Al12 cuboctahedra, corners with four equivalent Al(2)Ho4Al8 cuboctahedra, corners with six equivalent Al(3)Ho4Al8 cuboctahedra, edges with three equivalent Ho(1)Al12 cuboctahedra, edges with four equivalent Ho(2)Al12 cuboctahedra, edges with eight equivalent Al(3)Ho4Al8 cuboctahedra,  a faceface with one Ho(1)Al12 cuboctahedra,  a faceface with one Al(2)Ho4Al8 cuboctahedra, faces with three equivalent Ho(2)Al12 cuboctahedra, and faces with nine equivalent Al(3)Ho4Al8 cuboctahedra. There are a spread of Al(3)-Al(3) bond distances ranging from 2.95-3.07 Å.