La5Re3MgO16 crystallizes in the triclinic P-1 space group. Mg(1) is bonded to two equivalent O(3), two equivalent O(7), and two equivalent O(8) atoms to form MgO6 octahedra that share corners with two equivalent Re(1)O6 octahedra and corners with four equivalent Re(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 22-32°. There are three inequivalent La sites. In the first La site, La(1) is bonded in a 7-coordinate geometry to one O(2), one O(3), one O(4), one O(5), one O(6), and two equivalent O(7) atoms. In the second La site, La(2) is bonded in a 6-coordinate geometry to one O(2), one O(3), one O(4), one O(5), one O(6), and one O(8) atom. In the third La site, La(3) is bonded in a body-centered cubic geometry to two equivalent O(1), two equivalent O(2), two equivalent O(5), and two equivalent O(6) atoms. There are two inequivalent Re sites. In the first Re site, Re(1) is bonded to one O(2), one O(3), one O(5), one O(6), and two equivalent O(1) atoms to form ReO6 octahedra that share  a cornercorner with one Mg(1)O6 octahedra and  an edgeedge with one Re(1)O6 octahedra. The corner-sharing octahedral tilt angles are 32°. In the second Re site, Re(2) is bonded to two equivalent O(4), two equivalent O(7), and two equivalent O(8) atoms to form ReO6 octahedra that share corners with four equivalent Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 22-30°. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a 3-coordinate geometry to one La(3) and two equivalent Re(1) atoms. In the second O site, O(2) is bonded to one La(1), one La(2), one La(3), and one Re(1) atom to form corner-sharing OLa3Re tetrahedra. In the third O site, O(3) is bonded in a 4-coordinate geometry to one Mg(1), one La(1), one La(2), and one Re(1) atom. In the fourth O site, O(4) is bonded in a 3-coordinate geometry to one La(1), one La(2), and one Re(2) atom. In the fifth O site, O(5) is bonded in a 4-coordinate geometry to one La(1), one La(2), one La(3), and one Re(1) atom. In the sixth O site, O(6) is bonded in a 4-coordinate geometry to one La(1), one La(2), one La(3), and one Re(1) atom. In the seventh O site, O(7) is bonded in a 4-coordinate geometry to one Mg(1), two equivalent La(1), and one Re(2) atom. In the eighth O site, O(8) is bonded in a 3-coordinate geometry to one Mg(1), one La(2), and one Re(2) atom.
La5Re3MgO16 crystallizes in the triclinic P-1 space group. Mg(1) is bonded to two equivalent O(3), two equivalent O(7), and two equivalent O(8) atoms to form MgO6 octahedra that share corners with two equivalent Re(1)O6 octahedra and corners with four equivalent Re(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 22-32°. Both Mg(1)-O(3) bond lengths are 2.09 Å. Both Mg(1)-O(7) bond lengths are 2.08 Å. Both Mg(1)-O(8) bond lengths are 2.14 Å. There are three inequivalent La sites. In the first La site, La(1) is bonded in a 7-coordinate geometry to one O(2), one O(3), one O(4), one O(5), one O(6), and two equivalent O(7) atoms. The La(1)-O(2) bond length is 2.44 Å. The La(1)-O(3) bond length is 2.45 Å. The La(1)-O(4) bond length is 2.54 Å. The La(1)-O(5) bond length is 2.65 Å. The La(1)-O(6) bond length is 2.64 Å. There is one shorter (2.56 Å) and one longer (2.58 Å) La(1)-O(7) bond length. In the second La site, La(2) is bonded in a 6-coordinate geometry to one O(2), one O(3), one O(4), one O(5), one O(6), and one O(8) atom. The La(2)-O(2) bond length is 2.46 Å. The La(2)-O(3) bond length is 2.43 Å. The La(2)-O(4) bond length is 2.45 Å. The La(2)-O(5) bond length is 2.55 Å. The La(2)-O(6) bond length is 2.59 Å. The La(2)-O(8) bond length is 2.46 Å. In the third La site, La(3) is bonded in a body-centered cubic geometry to two equivalent O(1), two equivalent O(2), two equivalent O(5), and two equivalent O(6) atoms. Both La(3)-O(1) bond lengths are 2.60 Å. Both La(3)-O(2) bond lengths are 2.41 Å. Both La(3)-O(5) bond lengths are 2.58 Å. Both La(3)-O(6) bond lengths are 2.57 Å. There are two inequivalent Re sites. In the first Re site, Re(1) is bonded to one O(2), one O(3), one O(5), one O(6), and two equivalent O(1) atoms to form ReO6 octahedra that share  a cornercorner with one Mg(1)O6 octahedra and  an edgeedge with one Re(1)O6 octahedra. The corner-sharing octahedral tilt angles are 32°. The Re(1)-O(2) bond length is 1.97 Å. The Re(1)-O(3) bond length is 2.10 Å. The Re(1)-O(5) bond length is 1.94 Å. The Re(1)-O(6) bond length is 1.93 Å. There is one shorter (1.98 Å) and one longer (2.06 Å) Re(1)-O(1) bond length. In the second Re site, Re(2) is bonded to two equivalent O(4), two equivalent O(7), and two equivalent O(8) atoms to form ReO6 octahedra that share corners with four equivalent Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 22-30°. Both Re(2)-O(4) bond lengths are 1.93 Å. Both Re(2)-O(7) bond lengths are 2.04 Å. Both Re(2)-O(8) bond lengths are 1.99 Å. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a 3-coordinate geometry to one La(3) and two equivalent Re(1) atoms. In the second O site, O(2) is bonded to one La(1), one La(2), one La(3), and one Re(1) atom to form corner-sharing OLa3Re tetrahedra. In the third O site, O(3) is bonded in a 4-coordinate geometry to one Mg(1), one La(1), one La(2), and one Re(1) atom. In the fourth O site, O(4) is bonded in a 3-coordinate geometry to one La(1), one La(2), and one Re(2) atom. In the fifth O site, O(5) is bonded in a 4-coordinate geometry to one La(1), one La(2), one La(3), and one Re(1) atom. In the sixth O site, O(6) is bonded in a 4-coordinate geometry to one La(1), one La(2), one La(3), and one Re(1) atom. In the seventh O site, O(7) is bonded in a 4-coordinate geometry to one Mg(1), two equivalent La(1), and one Re(2) atom. In the eighth O site, O(8) is bonded in a 3-coordinate geometry to one Mg(1), one La(2), and one Re(2) atom.