. . . . "The seven classes divide into fourteen distinct modes of arrangement: three in the cubic system, one hexagonal, two tetragonal, one rhombohedral, four orthorhombic, two monoclinic and one triclinic." . "theoretical" . . "Formalization: one, contingent. Completeness is a theorem; that nature realises all fourteen is the empirical part." . "Related claim (analogy): Thompson explains the six-rayed hexactinellid spicule by vesicles packed in linear series, so that the spicule follows the edges of a system of cubes rather than of hexagons or dodecahedra: the arrangement he invokes is the cubic P mode of Bravais's fourteen. An analogy of packing between cells and lattice points, not a statement that the sponge is a crystal." . "There are fourteen distinct lattice modes" . "|\\text{Bravais lattices}| = 14" . . "Bravais A, “Mémoire sur les systèmes formés par des points distribués régulièrement sur un plan ou dans l'espace”, Journal de l'École Polytechnique 19 (cahier 33), 1850; read in Études cristallographiques, Gauthier-Villars, Paris, 1866 (1850); Mémoire sur les systèmes de points, § VI, pp. 95-98. Scope: All three-dimensional lattices." . "Bravais A. Mémoire sur les systèmes formés par des points distribués régulièrement sur un plan ou dans l'espace. Journal de l'École Polytechnique 19 (cahier 33), 1850; read in Études cristallographiques, Gauthier-Villars, Paris, 1866 (1850), 1-128" . "Auguste Bravais" . "1850"^^ . "The posthumous 1866 collection reprints the 1850 memoir on lattices and the 1851 memoir on polyhedra of crystalline form. French." . "Public domain (1850; collection 1866)." . "Mémoire sur les systèmes formés par des points distribués régulièrement sur un plan ou dans l'espace" . . . . "Reading copy of Mémoire sur les systèmes formés par des points distribués régulièrement sur un plan ou dans l'espace" . . . "delphisci crystals-and-form claim extractor" . . . . "Claude Fable 5.1" . . . . . . . . . . . . "Page 183 of the reading copy; paragraph 3259 of the normalised text 1850-bravais.txt (sha256 d7a7910b838d96a1c4b37d979c0ba877c254fd83a256922580fa367c168d3cbd), produced by build/fetch.py and checked by build/check-quotes.mjs. The text itself is not committed." . . . "Nous allons maintenant appliquer les formules du § IX à chacun des quatorze modes cristallins." . . "d7a7910b838d96a1c4b37d979c0ba877c254fd83a256922580fa367c168d3cbd" . "Checksum of the normalised one-paragraph-per-line text derived from the reading copy, not of the reading copy itself." . "crystals-and-form" . "2026-11-07T06:06:25.583Z"^^ . . . . . . "Auguste Bravais 1850 claim: There are fourteen distinct lattice modes" . . "RSA" . "MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAyFHtPB6p0mCjDozxlOY9CmO3nBm7Te3jFbXyLmM+G1tGe47Da0jYIbhkl9Oo1ZjxmCa3LCwlEqK8gj6hEIcL4ahW30JXh9HycfKVk1bugkzMEV15tJdTzAU3sGMFnbNsn43xY2LFLy45tApkRm5byEiM7oRRrooIdwoQKnP4Wzq/bfAoJ9qvW+MGkelyOTd1jbSt+KfmT7xKmDfWzAHddUlWwMX2QJOLxDaffOteTop6ZRgPiNmPJKA/S62Gac9XtSYT3oDkZ6/nr5cxxNLpOyxTf5FPISiCe11xYO/unYjY+mwnOfA8yhJIyx1l0O9I0vpOpn+E5TvyHJV+oSTrvwIDAQAB" . "XHxTVV83IwuJjtg+0RWF1I7BFYWGctkzSNj1kgGP3epoY+KDbO6Ma4vJhwkl2lSy1zWhgreZntzjPuj3y9s/HWndvAgNQw18JU6ijih9rHaLzAbmkiCbji29GYLdFlhl1optsWN1y5+dxFn6rg53Hj7Wo71PkUh0YsC37DfL4KG23I8dpm5P2QY7PDdIInClDwTABsNa/CTA/8kaTn4cO4YbQMt7gtsiKJVXO02IRy6L9UmOiUNQOOujjRzIQeHDC2jlQQFt7qAl3QRdLHhcsGeddP59ERUXcSpCxOGZQQpvBR+cvIbspESzc3pWv8cAXFkAwQe3YBSgHxLFKpKxvQ==" . . .