WordNet

(physical chemistry) a sample of matter in which substances in different phases are in equilibrium; "in a static system oil cannot be replaced by water on a surface"; "a system generating hydrogen peroxide"
instrumentality that combines interrelated interacting artifacts designed to work as a coherent entity; "he bought a new stereo system"; "the system consists of a motor and a small computer"
a group of independent but interrelated elements comprising a unified whole; "a vast system of production and distribution and consumption keep the country going" (同)scheme
a complex of methods or rules governing behavior; "they have to operate under a system they oppose"; "that language has a complex system for indicating gender" (同)system of rules
a group of physiologically or anatomically related organs or parts; "the body has a system of organs for digestion"
a procedure or process for obtaining an objective; "they had to devise a system that did not depend on cooperation"
the living body considered as made up of interdependent components forming a unified whole; "exercise helped him get the alcohol out of his system"
a six-sided polygon

PrepTutorEJDIC

〈C〉(関連した部分から成る)『体系』,系統,組織[網],装置 / 〈C〉(教育・政治などの)『制度』,機構;《the~》体制 / 〈C〉(思想・学問などの)『体系』,学説 / 〈C〉(…の)『方法』,方式,やり方《+of doing》 / 〈U〉正しい方針(筋道,順序) / 〈U〉《the~》(身体の)組織,系統 / 〈U〉《the~,one's~》身体,全身
六角形,六辺形
六角形の,六辺形の

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出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2015/12/09 02:32:11」(JST)

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An example of the hexagonal crystals, beryl
Hexagonal Hanksite crystal	Hexagonal lattice cell (P)

In crystallography, the hexagonal crystal system is one of the 7 crystal systems, the hexagonal lattice system is one of the 7 lattice systems, and the hexagonal crystal family is one of the 6 crystal families. They are closely related and often confused with each other, but they are not the same. The hexagonal lattice system consists of just one Bravais lattice type: the hexagonal one. The hexagonal crystal system consists of the 7 point groups such that all their space groups have the hexagonal lattice as underlying lattice. The hexagonal crystal family consists of the 12 point groups such that at least one of their space groups has the hexagonal lattice as underlying lattice, and is the union of the hexagonal crystal system and the trigonal crystal system.^[1]

In some cases, it is useful or instructive to redraw a hexagonal structure with orthohexagonal axes, wherein the b axis is redrawn at 90° to the a and c axes.

Graphite is an example of a crystal that crystallizes in the hexagonal crystal system.

Hexagonal lattice system

The hexagonal lattice system is one of the seven lattice systems, consisting of the hexagonal Bravais lattice. It is associated with 45 space groups whose underlying lattice has point group of order 24. It is often confused with the smaller hexagonal crystal system, which consists of the 27 space groups such that all space groups with the same point group are in the hexagonal lattice system, or with the larger hexagonal crystal family, consisting of the 52 space groups in either the hexagonal or rhombohedral lattice systems.

Crystal classes

The point groups (crystal classes) in this crystal system are listed below, followed by their representations in Hermann-Mauguin or international notation and Schoenflies notation, and mineral examples, if they exist.^[1]^[2]

#	Point group					Example	Space groups
#	Class	Intl	Schoen.	Orb.	Cox.	Example	Space groups
168-173	Hexagonal pyramidal	6	C₆	66	[6]⁺	nepheline, cancrinite	P6, P6₁, P6₅, P6₂, P6₄, P6₃
174	Trigonal dipyramidal	6	C_3h	3*	[2,3⁺]	Laurelite and Boric acid	P6
175-176	Hexagonal dipyramidal	6/m	C_6h	6*	[2,6⁺]	apatite, vanadinite	P6/m, P6₃/m
177-182	Hexagonal trapezohedral	622	D₆	226	[2,6]⁺	kalsilite and high quartz	P622, P6₁22, P6₅22, P6₂22, P6₄22, P6₃22
183-186	Dihexagonal pyramidal	6mm	C_6v	*66	[6]	greenockite, wurtzite ^[3]	P6mm, P6cc, P6₃cm, P6₃mc
187-190	Ditrigonal dipyramidal	6m2	D_3h	*223	[2,3]	benitoite	P6m2, P6c2, P62m, P62c
191-194	Dihexagonal dipyramidal	6/mmm	D_6h	*226	[2,6]	beryl	P6/mmm, P6/mcc, P6₃/mcm, P6₃/mmc

Hexagonal crystal family

The hexagonal crystal family consists of the 12 point groups such that at least one of their space groups has the hexagonal lattice as underlying lattice, and is the union of the hexagonal crystal system and the trigonal crystal system. There are 50 space groups associated with it, which are exactly those whose Bravais lattice is either hexagonal or rhombohedral.

References

^ ^a ^b DANA, James Dwight; Hurlbut, Cornelius Searle (1959). Dana's Manual of Mineralogy. (17th Edition.). New York: Chapman Hall. p. 78–89.
^ "Crystallography". Webmineral.com. Retrieved 2014-08-03.
^ "Minerals in the Hexagonal crystal system, Dihexagonal Pyramidal class (6mm)". Mindat.org. Retrieved 2014-08-03.

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