Ultramarine differs from other inorganic pigments in that it does not contain any transition metals. It is the sulfur species that confer the colour: S3•− (blue ultramarine), S2•− (yellow ultramarine) or S4 (red ultramarine). Green ultramarine contains both S2•− and S3•− .
You’d think that by now they should know what the structure of ultramarine is. But no. In the Inorganic Crystal Structure Database I’ve found only two structures called “ultramarine” (ICSD 27523 and 27524), both associated with a paper from 1936 . The composition of ICSD 27523 is given as Na8Al6Si6O24S2.5·(H2O)0.6. The structure (see figure below) is an aluminosilicate cage containing sodium cations and beautiful octahedral sulfur clusters. Wait a minute. S7 clusters? Never heard about those before.
A more recent structure of deuterated lazurite, Na7.5Al6Si6O24S4.5·(D2O)0.5 (ICSD 63022), also featuring S7 octahedra, provided an explanation. The authors  wrote that
to accommodate the indications emerging from the difference maps, the octahedral model of sulfur occupancy was modified to reproduce a more even density inside cage by adding a further sulfur to the hollow octahedral shell, with sulfur occupancies rescaled accordingly to maintain S3 overall.I feel relieved if slightly disappointed.
- Landman, A.A. (2003) Aspects of solid-state chemistry of fly ash and ultramarine pigments. Doctoral Thesis, University of Pretoria.
- Podschus, E., Hofmann, U. & Leschewski, K. (1936) Röntgenographische Strukturuntersuchung von Ultramarinblau und seinen Reaktionsprodukten. Zeitschrift für anorganische und allgemeine Chemie 228, 305—333.
- Tarling, S.E., Barnes, P. and Klinowski, J. (1988) The structure and Si,Al distribution of the ultramarines. Acta Crystallographica B44, 128—135.