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A Standardized Japanese Nomenclature for Crystal Forms

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A Standardized Japanese Nomenclature for Crystal Forms MINERALOGICAL JOURNAL, VOL. 4, No. 4, pp. 291-298, FEB., 1565 A STANDARDIZED JAPANESE NOMENCLATURE FOR CRYSTAL FORMS J. D. H. DONNAY and HIROSHI TAKEDA The Johns Hopkins University, Baltimore, Maryland, U. S. A. with the help of many Japanese crystallographers ABSTRACT The system of the crystal-form names according to the proposal of the Fedorov Institute is explained, and adequate Japanese equivalents are given. Introduction Efforts have been made in the past to standardize the names of the crystal forms. Particularly noteworthy were the proposals of the Fedorov Institute (Boldyrev 1925, 1936) and of Rogers (1935), both of which are modifications of the Groth nomenclature. Recently the Committee on Nomenclature of the French Society of Mineralogy and Crystallography have re-examined the problem (see Donnay and Curien 1959) and have essentially proposed the sys tem of the Fedorov Institute as a basis for possible international agreement. In view of these developments, it was thought that it would be useful to see if the Japanese nomenclature of crystal forms could be adapted to the Federov-Institute system. The present paper first explains the system of form names, and attempts to give adequate Japanese equivalents, for non-cubic and then for cubic forms. Then the English names are listed with syno nyms, together with the various Japanese terms that have been used. When there is more than one Japanese name, they are listed in a tentative order of preference, arrived at after many inquiries and consultations. Finally a key to the crystal forms in the 32 point 292 A Standardized Japanese Nomenclature for Crystal Forms groups is given. The reader can thus check his own derivation of the forms in each symmetry group. Acknowledgements The senior author's sincere thanks are due, first of all, to Dr. Hiroshi Takeda, for his infinite patience in teaching him the rudi ments of the Japanese language and for his very active co-operation in setting up a set of Japanese terms based on the same principles as the nomenclature of the Fedorov Institute. Dr. Nobuo Morimoto and Dr. Dorothy Mizoguchi gave very good philological advice. The Japanese textbook of Toshio Sudo (1963), kindly provided by Dr. Takeshi Tomisaka, was of great help in that it permitted comparison with a system of nomenclature already in use and many of its names turned out to be the preferred ones in the end. Finally Professor R. Sadanaga and his colleagues at the University of Tokyo have given us the benefit of their criticism. Description of the 47 Crystal Forms The 32 non-cubic forms. The form may have only one face (monohedron, ichimentai). If a form has two faces, they may either intersect (dihedron, nimentai)* or be parallel (parallelohedron, hekomentai, pinacoid, takumentai). Three series of forms may have 3, 4, 6, 8, 12, 16 or 24 faces ; they are the prisms (chumentai), pyramids (suimentai) and dipyramids (fukusuimentai). The faces of a prism are parallel to a certain direction ; they intersect along parallel edges. The faces of a pyramid come to a point; they are equally inclined on a certain direction, which is the axis of the pyramid. A dipyramid, also called bipyramid or double pyramid, is a doubly terminated form that consists of two identical pyramids placed end to end, so that one is the mirror image * The terms dome (himentai) and sphenoid (setsumentai) are to be abandoned. J. D. H. DONNAY and H. TAKEDA 293 of the other. Prisms are differentiated on the basis of their cross - sections ; so are the pyramids and dipyramids . The cross-section may be an equilateral triangle1) (trigonal prism, sanpo chumentai) , a rhomb or lozenge (rhombic prism, shaho chumentai), a square (tetra gonal prism, seiho chumentai), a hexagon (hexagonal prism, roppo chumentai). If you replace each side of an equilateral triangle by two equal lines making a very obtuse angle, the trigon becomes a ditrigon (fukusanpo). The ditetragon (fukuseiho) and dihexagon (fuku roppo) are defined likewise. These polygons, in which all sides are equal and alternate angles are equal can also be cross-sections of prisms, pyramids and dipyramids. Besides the dipyramids, there are two other kinds of doubly terminated forms. They can be visualized as follows. Take two identical pyramids, one pointing up, the other down, with their axes in coincidence, and rotate the one with respect to the other, through an angle ƒÆ, about their common axis. If ƒÆ is equal to half the period of the symmetry axis of the pyramid, the resulting form is a rhombo hedron (shahomentai)*, or a scalenohedron (hutohensankakumentai, hensankakumentai, or better sanpenmentai). If ƒÆ is not equal to the half period, the form is a trapezohedron (nitohenshihenkementai, hen shikakumentai, or better shihenmentai). These names recall the shape of the face: rhomb (shaho), scalene triangle (hutohensankakuke), 1) The Japanese mathematical terms for: (1) equilateral triangle, (2) rhomb, (3) square, and (4) hexagon are: (1) sei sankakuke=sei sankakke, (2) ryoke, (3) sei shikakuke=sei shikakke=seihoke, and (4) sei rokkakuke= sei rokkakke. Crystallographers, however, have been using other adjectives to designate the crystal systems: (1) sanpo-, (2) shaho-, (3) seiho-, and (4) roppo-. In a nomenclature of crystal forms, it would seem preferable to use the crystallographers', rather than the mathematicians', terms. * This rhomb does not have 60•‹ and 120•‹ angles . It is a shahoke, not a ryoke. 294 A Standardized Japanese Nomenclature for Crystal Forms trapezoid (nitohenshihenke). (A trapezoid2) is an isosecles quadrilateral.) In a rhombohedron the starting pyramids are trigonal. There are two kinds of scalenohedra, as the starting pyramids may be rhombic or ditrigonal. The corresponding forms are called tetragonal scaleno- hedron (seiho sanpenmentai) and hexagonal scalenohedron (roppo san penmentai) according as the shape of their projection onto a plane perpendicular to the principal symmetry axis (4 or 3) is a square or a hexagon. There are three trapezohedra, each of which is named after the cross-section of one of the terminations: trigonal (sanpo), tetragonal (seiho), or hexagonal (roppo) trapezohedron (shihenmentai). Finally there remain two non-cubic forms. They are the irregular tetrahedra: the rhombic tetrahedron (shaho shimentai) and the tetra gonal tetrahedron (seiho shimentai), in which the cross-section at mid height is a rhomb or a square respectively. Note that these tetra hedra can be visualized as formed by two dihedra end to end, one of them rotated through ƒÆ with respect to the other: ƒÆ=90•‹ gives the tetragonal tetrahedron, ƒÆ•‚90•‹ gives the rhombic tetrahedron. The 15 cubic forms. The tetrahedron (shimentai) is the regular tetrahedron (sei shi mentai). If we let each face of the tetrahedron be replaced by a low trigonal pyramid and let the faces of the four pyramids be ex tended until they meet, we obtain a 12-face polyhedron, which may be a trigon-tritetrahedron (sanpen-san-shimentai), a tetragon-tritetra- 2) Euclid's "trapezion" was any quadrilateral (futohenshihenke). Pro clus (ca. 450 A. D.) distinguished trapezium (teke=daike), with two parallel sides, from trapezoid (nitohenshihenke), with two equal sides. A special case of the latter is the bi-isosceles quadrilateral or deltoid (fukunitohen- shihenke), which bears the same relation to a parallelogram as the trapezoid to the trapezium and which, therefore, has also been called a "counter- parallelogram". Deltoid-shaped faces are found in two forms of the cubic system, one of which (tetragon-trioctahedron) has been called trapezohedron, the other (tetragon-tritetrahedron) is also known as deltohedron. The word deltoid comes from the fact (or the fancy!) that a counter-parallelogram resembles the Greek letter delta (ƒ¢). J. D. H. DONNAY and H. TAKEDA 295 hedron (shihen-san-shimentai), or a pentagon-tritetrahedron (gohen-san- shimentai), according as the faces have 3, 4 or 5 sides. Note that the face is an isosceles triangle (nitohen sankakuke), a deltoid (fuku nitohen shihenke), or a pentagon in which two pairs of consecutive sides are equal (a, a, b, b, c). Because the edges of the original tetrahedron are retained in the trigon-tritetrahedron, the latter has been called, in French, "tetraedre pyramide" (suishimentai). The tetragon-tritetrahedron has been designated "deltohedron." If a low ditrigonal pyramid replaces each face of a tetrahedron, the hexatetra hedron (roku-shimentai) is obtained. From the octahedron (hachimentai) the following 24-face forms are likewise derived: the trigon-trioctahedron (sanpen-san-hachimen- tai), which is the French "octaedre pyramide" (suihachimentai), the tetragon-trioctahedron (shihen-san-hachimentai), which had been called "trapezohedron " and "deltoid icositetrahedron" , and the pentagon- trioctahedron (gohen-san-hachimentai). In the latter the low trigonal pyramids that replace the original octahedral faces have all turned in the same sense, either clockwise or counterclockwise, around the 3-axes; this is why the form has also been called "gyroid." Re placing each face of the octahedron by a low ditrigonal pyramid results in a hexaoctahedron (roku-hachimentai). The cube (rippotai) or hexahedron (rokumentai) likewise gives rise to the tetrahexahedron (shi-rokumentai), which is the French "cube pyramide" (suirippotai) , and to the dihexahedron (fuku-roku- mentai), which is an (irregular) "pentagon-dodecahedron" (gohen- junimentai), different from the regular dodecahedron of Geometry (gokaku-junimentai). The dihexahedron in turn gives rise to the didodecahedron (fuku-junimentai). The rhomb-dodecahedron (ryo-junimentai) does not give rise to any other form. 296 A Standardized Japanese Nomenclature for Crystal Forms List of the 47 Crystal Forms 1. Monohedron, 1. Ichimentai, pedion tanmentai 2. Parallelohedron, 2. Hekomentai, pinakoid takumentai 3. Dihedron 3. Nimentai 4. Rhombic prism 4. Shaho chumentai, shaho-chutai 5. Trigonal prism 5. Sanpo chumentai, sanpo-chutai 6. Ditrigonal prism 6. Fukusanpo chumentai, fuku-sanpo-chutai 7. Tetragonal prism 7. Seiho chumentai, seiho-chutai 8. Ditetragonal prism 8. Fukuseiho chumentai, fuku-seiho-chutai 9.
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