Na4Al3Si3SO16 crystallizes in the cubic P-43n space group. Na(1) is bonded to one O(1) and six equivalent O(2) atoms to form distorted NaO7 hexagonal pyramids that share corners with six equivalent Na(1)O7 hexagonal pyramids,  a cornercorner with one S(1)O4 tetrahedra, edges with three equivalent Al(1)O4 tetrahedra, and edges with three equivalent Si(1)O4 tetrahedra. Al(1) is bonded to four equivalent O(2) atoms to form AlO4 tetrahedra that share corners with four equivalent Si(1)O4 tetrahedra and edges with four equivalent Na(1)O7 hexagonal pyramids. Si(1) is bonded to four equivalent O(2) atoms to form SiO4 tetrahedra that share corners with four equivalent Al(1)O4 tetrahedra and edges with four equivalent Na(1)O7 hexagonal pyramids. S(1) is bonded to four equivalent O(1) atoms to form SO4 tetrahedra that share corners with four equivalent Na(1)O7 hexagonal pyramids. There are two inequivalent O sites. In the first O site, O(1) is bonded in a distorted single-bond geometry to one Na(1) and one S(1) atom. In the second O site, O(2) is bonded in a 3-coordinate geometry to two equivalent Na(1), one Al(1), and one Si(1) atom.
Na4Al3Si3SO16 crystallizes in the cubic P-43n space group. Na(1) is bonded to one O(1) and six equivalent O(2) atoms to form distorted NaO7 hexagonal pyramids that share corners with six equivalent Na(1)O7 hexagonal pyramids,  a cornercorner with one S(1)O4 tetrahedra, edges with three equivalent Al(1)O4 tetrahedra, and edges with three equivalent Si(1)O4 tetrahedra. The Na(1)-O(1) bond length is 2.87 Å. There are three shorter (2.42 Å) and three longer (2.90 Å) Na(1)-O(2) bond lengths. Al(1) is bonded to four equivalent O(2) atoms to form AlO4 tetrahedra that share corners with four equivalent Si(1)O4 tetrahedra and edges with four equivalent Na(1)O7 hexagonal pyramids. All Al(1)-O(2) bond lengths are 1.75 Å. Si(1) is bonded to four equivalent O(2) atoms to form SiO4 tetrahedra that share corners with four equivalent Al(1)O4 tetrahedra and edges with four equivalent Na(1)O7 hexagonal pyramids. All Si(1)-O(2) bond lengths are 1.63 Å. S(1) is bonded to four equivalent O(1) atoms to form SO4 tetrahedra that share corners with four equivalent Na(1)O7 hexagonal pyramids. All S(1)-O(1) bond lengths are 1.49 Å. There are two inequivalent O sites. In the first O site, O(1) is bonded in a distorted single-bond geometry to one Na(1) and one S(1) atom. In the second O site, O(2) is bonded in a 3-coordinate geometry to two equivalent Na(1), one Al(1), and one Si(1) atom.