A Standardized Japanese Nomenclature for Crystal Forms

Home , Hexagonal pyramid, Hexahedron, Icositetrahedron, Rhombohedron, Trapezohedron

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-hachimentai), 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-rokumentai), 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. Hexagonal prism 9. Roppo chumentai, roppo-chutai 10. Dihexagonal prism 10. Fukuroppo chumentai, fuku-roppo-chutai 11. Rhombic pyramid 11. Shaho suimentai, shaho-suitai 12. Trigonal pyramid 12. Sanpo suimentai, sanpo-suitai 13. Ditrigonal pyramid 13. Fukusanpo suimentai, fuku-sanpo-suitai 14. Tetragonal pyramid 14. Seiho suimentai, seiho-suitai 15. Ditetragonal pyramid 15. Fukuseiho suimentai, fuku-seiho-suitai 16. Hexagonal pyramid 16. Roppo suimentai, roppo-suitai 17. Dihexagonal pyramid 17. Fukuroppo suimentai, fuku-roppo-suitai 18. Rhombic dipyramid 18. Shaho fukusuimentai, shaho-ryosuitai 19. Trigonal dipyramid 19. Sanpo fukusuimentai, sanpo-ryosuitai 20. Ditrigonal dipyramid 20. Fukusanpo fukusuimentai, fuku-sanpo-ryosuitai 21. Tetragonal dipyramid 21. Seiho fukusuimentai, seiho-ryosuitai 22. Ditetragonal dipyramid 22. Fukuseiho fukusuimentai, fuku-seiho-ryosuitai 23. Hexagonal dipyramid 23. Roppo fukusuimentai, roppo-ryosuitai 24. Dihexagonal dipyramid 24. Fukuroppo fukusuimentai, fuku-roppo-ryosuitai J. D. H. DONNAY and H. TAKEDA 297

25. Trigonal trapezohedron 25. Sanpo shihenmentai, sanpo henshikakumentai, hen-rokumentai 26. Tetragonal trapezohedron 26. Seiho shihenmentai, seiho henshikakumentai, hen-hachimentai

27. Hexagonal trapezohedron 27. Roppo shihenmentai, roppo henshikakumentai, hen-saikakumentai

28. Tetragonal scalenohedron 28. Seiho sanpenmentai, seiho-hen-sankakumentai

29. Hexagonal scalenohedron, 29. Roppo sanpenmentai, ditrigonal scalenohedron roppo-hen-sankakumentai, fuku-sanpo-hen-sankakumentai

30. Rhombohedron 30. Shahomentai, ryomentai 31. Rhombic tetrahedron, 31. Shaho shimentai, rhombic disphenoid shaho-ryosetsutai 32. Tetragonal tetrahedron, 32. Seiho shimentai, tetragonal disphenoid seiho-ryosetsutai 33. Hexahedron, 33. Rokumentai, cube rippotai, sei-rokumentai

34. Tetrahexahedron, 34. Shi-rokumentai, French "cube pyramide" suirippotai 35. Rhomb-dodecahedron 35. Ryo-junimentai

36. Octahedron 36. Hachimentai, sei-hachimentai

37. Trigon-trioctahedron, 37. Sanpen-san-hachimentai, French "octaedre pyramide", suihachimentai, trisoctahedron san-hachimentai

38. Tetragon-trioctahedron, 38. Shihen-san-hachimentai, trapezohedron, deltoid-icositetrahedron hen-ryo-san-hachimentai 39. Pentagon-trioctahedron, 39. Gohen-san-hachimentai,•c gyroid, pentagon-icositetrahedron gokaku-san-hachimentai 40. Hexaoctahedron, 40. Roku-hachimentai hexoctahedron

41. Tetrahedron 41. Shimentai

42. Tetragon-tritetrahedron, 42. Shihen-san-shimentai,•c deltohedron, deltoid-dodecahedron hen-ryo-junimentai

43. Trigon-tritetrahedron, 43. Sanpen-san-shimentai, French "tetraedre pyramide", suishimentai, tristetrahedron san-shimentai

44. Pentagon-tritetrahedron, 44. Gohen-san-shimentai, •c tetartoid, tetrahedral pentagon- hen-gokaku-junimentai dodecahedron 298 A Standardized Japanese Nomenclature for Crystal Forms

45. Hexatetrahedron, 45. Roku-shimentai hextetrahedron 46. Dihexahedron, 46. Fuku-rokumentai, pentagon-dodecahedron, gohen-junimentai, pyritohedron gokaku-junimentai 47. Didodecahedron, 47. Fuku-junimentai, diploid henpo-nijushimentai

REFERENCES

Boldirew, A. K. (1925). Die vom Fedorow-Institut angenommene kristallo- graphische Nomenklatur. Z. Kristallogr., 62, 145-150. Boldyrev, A. K. (1936). Are there 47 or 48 simple forms possible on crystals? Amer. Min., 21, 731-734. Donnay, J. D. H. and Curien, H. (1958). Nomenclature des 47 formes cristal- lines. Bull. Soc. fr. Min. Crist., 81, xliv-xlvii. Rogers, A. F. (1935). A tabulation of crystal forms and discussion of form names. Amer. Min., 20, 838-851. Shafranovskii, I. I., Mokievskii, V.A. and Stulov. N. N. (1959). Disskusiya o nomenklature kristallograficheskikh form vo frantsuzskom mineralogiche- skom obshchestve. Zapiski vsesoyuznogo mineralogicheskogo obshchestva, 88, 492-495. Sudo, Toshio (1963). Kobutsugaku-honron (Principles of Mineralogy). Asa kura Publ. Co., Japan.

Manuscript received 13 February 1965.

COMMENTS ADDED IN PROOF

Professor R. Sadanaga kindly points out that, in the above terminology, a form name is intended to designate a set of symmetry-related (equivalent) faces, rather than the shape of a geometrical solid. It follows that chumen tai is preferred to chutai, rokumentai to rippotai, etc. The same problem is faced in other languages: hexahedron is a better crystallographic name than cube, which is the usual geometrical term.