Mg23Gd6C crystallizes in the cubic Fm-3m space group. There are four inequivalent Mg sites. In the first Mg site, Mg(2) is bonded in a 13-coordinate geometry to one Mg(4), three equivalent Mg(1), three equivalent Mg(2), three equivalent Mg(3), and three equivalent Gd(1) atoms. In the second Mg site, Mg(3) is bonded to four equivalent Mg(1), four equivalent Mg(2), and four equivalent Gd(1) atoms to form distorted MgGd4Mg8 cuboctahedra that share corners with four equivalent Mg(3)Gd4Mg8 cuboctahedra, corners with eight equivalent Mg(1)Gd3Mg9 cuboctahedra, edges with two equivalent C(1)Gd6 octahedra, faces with eight equivalent Mg(1)Gd3Mg9 cuboctahedra, and faces with eight equivalent Mg(3)Gd4Mg8 cuboctahedra. In the third Mg site, Mg(4) is bonded in a body-centered cubic geometry to eight equivalent Mg(2) atoms. In the fourth Mg site, Mg(1) is bonded to three equivalent Mg(1), three equivalent Mg(2), three equivalent Mg(3), and three equivalent Gd(1) atoms to form distorted MgGd3Mg9 cuboctahedra that share corners with six equivalent Mg(1)Gd3Mg9 cuboctahedra, corners with six equivalent Mg(3)Gd4Mg8 cuboctahedra, faces with six equivalent Mg(1)Gd3Mg9 cuboctahedra, faces with six equivalent Mg(3)Gd4Mg8 cuboctahedra, and  a faceface with one C(1)Gd6 octahedra. Gd(1) is bonded in a single-bond geometry to four equivalent Mg(1), four equivalent Mg(2), four equivalent Mg(3), and one C(1) atom. C(1) is bonded to six equivalent Gd(1) atoms to form CGd6 octahedra that share edges with twelve equivalent Mg(3)Gd4Mg8 cuboctahedra and faces with eight equivalent Mg(1)Gd3Mg9 cuboctahedra.
Mg23Gd6C crystallizes in the cubic Fm-3m space group. There are four inequivalent Mg sites. In the first Mg site, Mg(2) is bonded in a 13-coordinate geometry to one Mg(4), three equivalent Mg(1), three equivalent Mg(2), three equivalent Mg(3), and three equivalent Gd(1) atoms. The Mg(2)-Mg(4) bond length is 2.97 Å. All Mg(2)-Mg(1) bond lengths are 3.16 Å. All Mg(2)-Mg(2) bond lengths are 3.43 Å. All Mg(2)-Mg(3) bond lengths are 3.13 Å. All Mg(2)-Gd(1) bond lengths are 3.74 Å. In the second Mg site, Mg(3) is bonded to four equivalent Mg(1), four equivalent Mg(2), and four equivalent Gd(1) atoms to form distorted MgGd4Mg8 cuboctahedra that share corners with four equivalent Mg(3)Gd4Mg8 cuboctahedra, corners with eight equivalent Mg(1)Gd3Mg9 cuboctahedra, edges with two equivalent C(1)Gd6 octahedra, faces with eight equivalent Mg(1)Gd3Mg9 cuboctahedra, and faces with eight equivalent Mg(3)Gd4Mg8 cuboctahedra. All Mg(3)-Mg(1) bond lengths are 2.91 Å. All Mg(3)-Gd(1) bond lengths are 3.70 Å. In the third Mg site, Mg(4) is bonded in a body-centered cubic geometry to eight equivalent Mg(2) atoms. In the fourth Mg site, Mg(1) is bonded to three equivalent Mg(1), three equivalent Mg(2), three equivalent Mg(3), and three equivalent Gd(1) atoms to form distorted MgGd3Mg9 cuboctahedra that share corners with six equivalent Mg(1)Gd3Mg9 cuboctahedra, corners with six equivalent Mg(3)Gd4Mg8 cuboctahedra, faces with six equivalent Mg(1)Gd3Mg9 cuboctahedra, faces with six equivalent Mg(3)Gd4Mg8 cuboctahedra, and  a faceface with one C(1)Gd6 octahedra. All Mg(1)-Mg(1) bond lengths are 3.27 Å. All Mg(1)-Gd(1) bond lengths are 3.41 Å. Gd(1) is bonded in a single-bond geometry to four equivalent Mg(1), four equivalent Mg(2), four equivalent Mg(3), and one C(1) atom. The Gd(1)-C(1) bond length is 2.57 Å. C(1) is bonded to six equivalent Gd(1) atoms to form CGd6 octahedra that share edges with twelve equivalent Mg(3)Gd4Mg8 cuboctahedra and faces with eight equivalent Mg(1)Gd3Mg9 cuboctahedra.