MgCr4O12 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(1), one O(10), one O(11), and one O(8) atom to form MgO4 tetrahedra that share  a cornercorner with one Cr(1)O4 tetrahedra,  a cornercorner with one Cr(2)O4 tetrahedra,  a cornercorner with one Cr(3)O4 tetrahedra, and  a cornercorner with one Cr(4)O4 tetrahedra. There are four inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(1), one O(2), one O(4), and one O(6) atom to form CrO4 tetrahedra that share  a cornercorner with one Mg(1)O4 tetrahedra and corners with two equivalent Cr(2)O4 tetrahedra. In the second Cr site, Cr(2) is bonded to one O(3), one O(4), one O(6), and one O(8) atom to form CrO4 tetrahedra that share  a cornercorner with one Mg(1)O4 tetrahedra and corners with two equivalent Cr(1)O4 tetrahedra. In the third Cr site, Cr(3) is bonded to one O(10), one O(5), one O(7), and one O(9) atom to form CrO4 tetrahedra that share  a cornercorner with one Mg(1)O4 tetrahedra and corners with two equivalent Cr(4)O4 tetrahedra. In the fourth Cr site, Cr(4) is bonded to one O(11), one O(12), one O(7), and one O(9) atom to form CrO4 tetrahedra that share  a cornercorner with one Mg(1)O4 tetrahedra and corners with two equivalent Cr(3)O4 tetrahedra. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a bent 150 degrees geometry to one Mg(1) and one Cr(1) atom. In the second O site, O(2) is bonded in a single-bond geometry to one Cr(1) atom. In the third O site, O(3) is bonded in a single-bond geometry to one Cr(2) atom. In the fourth O site, O(4) is bonded in a bent 150 degrees geometry to one Cr(1) and one Cr(2) atom. In the fifth O site, O(5) is bonded in a single-bond geometry to one Cr(3) atom. In the sixth O site, O(6) is bonded in a bent 150 degrees geometry to one Cr(1) and one Cr(2) atom. In the seventh O site, O(7) is bonded in a bent 150 degrees geometry to one Cr(3) and one Cr(4) atom. In the eighth O site, O(8) is bonded in a bent 150 degrees geometry to one Mg(1) and one Cr(2) atom. In the ninth O site, O(9) is bonded in a bent 150 degrees geometry to one Cr(3) and one Cr(4) atom. In the tenth O site, O(10) is bonded in a bent 150 degrees geometry to one Mg(1) and one Cr(3) atom. In the eleventh O site, O(11) is bonded in a bent 150 degrees geometry to one Mg(1) and one Cr(4) atom. In the twelfth O site, O(12) is bonded in a single-bond geometry to one Cr(4) atom.
MgCr4O12 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(1), one O(10), one O(11), and one O(8) atom to form MgO4 tetrahedra that share  a cornercorner with one Cr(1)O4 tetrahedra,  a cornercorner with one Cr(2)O4 tetrahedra,  a cornercorner with one Cr(3)O4 tetrahedra, and  a cornercorner with one Cr(4)O4 tetrahedra. The Mg(1)-O(1) bond length is 1.97 Å. The Mg(1)-O(10) bond length is 1.97 Å. The Mg(1)-O(11) bond length is 1.98 Å. The Mg(1)-O(8) bond length is 1.98 Å. There are four inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(1), one O(2), one O(4), and one O(6) atom to form CrO4 tetrahedra that share  a cornercorner with one Mg(1)O4 tetrahedra and corners with two equivalent Cr(2)O4 tetrahedra. The Cr(1)-O(1) bond length is 1.67 Å. The Cr(1)-O(2) bond length is 1.59 Å. The Cr(1)-O(4) bond length is 1.85 Å. The Cr(1)-O(6) bond length is 1.85 Å. In the second Cr site, Cr(2) is bonded to one O(3), one O(4), one O(6), and one O(8) atom to form CrO4 tetrahedra that share  a cornercorner with one Mg(1)O4 tetrahedra and corners with two equivalent Cr(1)O4 tetrahedra. The Cr(2)-O(3) bond length is 1.59 Å. The Cr(2)-O(4) bond length is 1.71 Å. The Cr(2)-O(6) bond length is 1.73 Å. The Cr(2)-O(8) bond length is 1.66 Å. In the third Cr site, Cr(3) is bonded to one O(10), one O(5), one O(7), and one O(9) atom to form CrO4 tetrahedra that share  a cornercorner with one Mg(1)O4 tetrahedra and corners with two equivalent Cr(4)O4 tetrahedra. The Cr(3)-O(10) bond length is 1.67 Å. The Cr(3)-O(5) bond length is 1.59 Å. The Cr(3)-O(7) bond length is 1.85 Å. The Cr(3)-O(9) bond length is 1.85 Å. In the fourth Cr site, Cr(4) is bonded to one O(11), one O(12), one O(7), and one O(9) atom to form CrO4 tetrahedra that share  a cornercorner with one Mg(1)O4 tetrahedra and corners with two equivalent Cr(3)O4 tetrahedra. The Cr(4)-O(11) bond length is 1.66 Å. The Cr(4)-O(12) bond length is 1.59 Å. The Cr(4)-O(7) bond length is 1.71 Å. The Cr(4)-O(9) bond length is 1.73 Å. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a bent 150 degrees geometry to one Mg(1) and one Cr(1) atom. In the second O site, O(2) is bonded in a single-bond geometry to one Cr(1) atom. In the third O site, O(3) is bonded in a single-bond geometry to one Cr(2) atom. In the fourth O site, O(4) is bonded in a bent 150 degrees geometry to one Cr(1) and one Cr(2) atom. In the fifth O site, O(5) is bonded in a single-bond geometry to one Cr(3) atom. In the sixth O site, O(6) is bonded in a bent 150 degrees geometry to one Cr(1) and one Cr(2) atom. In the seventh O site, O(7) is bonded in a bent 150 degrees geometry to one Cr(3) and one Cr(4) atom. In the eighth O site, O(8) is bonded in a bent 150 degrees geometry to one Mg(1) and one Cr(2) atom. In the ninth O site, O(9) is bonded in a bent 150 degrees geometry to one Cr(3) and one Cr(4) atom. In the tenth O site, O(10) is bonded in a bent 150 degrees geometry to one Mg(1) and one Cr(3) atom. In the eleventh O site, O(11) is bonded in a bent 150 degrees geometry to one Mg(1) and one Cr(4) atom. In the twelfth O site, O(12) is bonded in a single-bond geometry to one Cr(4) atom.