Mineralogy. Symmetry views. Classification of crystals by the form symmetries.

Symmetry views. Classification of crystals by the form symmetries. Symmetry is natural repeatability in a location of subjects or their parts on a plain or in room. In the nature symmetry is displayed in a major variety and is specially characteristic for crystals. It is their major and particular property reflective legitimacy of interior.

Let's view symmetry devices.

1. Plane of symmetry. It is an imagined plain which one divides a figure on two equal parts so, that one of parts is a specular reflexion another. The plane of symmetry is designated R.Esli's by letter of planes of symmetry in the yielded crystal a little before a plain label their number is put, for example - 3Р, three planes of symmetry. In crystals there can be one, two, three, four, five, six, seven and nine planes of symmetry. Many crystals at all have no any plane of symmetry.
2. Symmetry centre. The symmetry centre terms such point in a figure, at holding through which one any straight line will meet the identical and revertively laied out parts of a figure on spacing interval equal from it. The symmetry centre is designated by the letter With (or i). If each crystal face has to itself equal, though and revertively laied out facet the yielded crystal possesses symmetry centre. Some crystals can not have symmetry centre.
3. Symmetry axes. The symmetry axis terms an imagined straight line, at rotational displacement round which one always on the same angle there is a combination of equal parts of a figure. At rotational displacement on 360 ° combination of facets in different crystals probably two, three, four or six times (i.e. at each rotational displacement on 180, 120, 90 and 60 °). The Symmetry axis is designated by letter L, the fulcrum order demonstrates, how many time at rotational displacement on 360 ° will originate combination of each of facets. So in crystals fulcrums second L2, the third L3, the fourth L4 and the sixth L6 orders are possible. Symmetry axes L3, L4, L6 are termed as symmetry axes of the higher order. Symmetry axes of the fifth and above the sixth order owing to legitimacy of interior of crystals are impossible. The Symmetry axis of maiden order L1 demonstrates, that for combination of a figure with its original standing it is necessary to make rotational displacement on 360 °; It corresponds to the complete lack of symmetry for any subject at rotational displacement on 360 ° round any real direction will be mated with itself.
4. Inversion symmetry axes. The inversion symmetry axis (Li) terms an imagined straight line, at rotational displacement round which one on some certain angle and reflex in a central point of a figure (as at symmetry centre) the figure is mated with itself, i.e. the inversion fulcrum introduces combined action of a symmetry axis and symmetry centre. Thus it is necessary to score, that on crystals the symmetry centre can not be displayed in the form of an independent device of symmetry.

In crystals 32 combinations of elements symmetries (32 views of symmetry) are possible only. Symmetry views combine in syngonies or systems. In total distinguish seven syngonies.

Triclinic, monoclinic and trimetric syngonies are termed as the lowest because they have no symmetry axes above the second order (L2).

Trigonal, tetragonal and hexagonal syngonies are termed as averages; they have one symmetry axis of the higher order (L3, L4 or Li4), L6 (or Li6).

The cubic syngony has some symmetry axes of the higher order (L3, L4 or Li4); it is termed as the higher syngony.

Simple shapes and their combinations. The review of simple shapes on syngonies. Plurality of facets which can be gained from an initial facet at activity of all of elements symmetries of the given crystal, is termed as the simple shape. Hence, it is such figure in a crystal which all facets at the uniform development on the size and the shape are identical. At a crystal there can be one, two or several simple shapes. The combination of two or several simple shapes is termed as a combination.

Simple shapes can close and not close spaces; they are accordingly termed unclosed and closed.

So, for example, the zircon crystal represents a combination of two simple shapes: a tetragonal prism and a tetragonal dipyramid. The prism is the open shape as it does not close space, a dipyramid - the closed shape as it completely closes space, let even on continuation of the facets.

To distinguish on crystals simple shapes, it is necessary to know a rule, first of all: how many on uniformly developed crystal of different facets, will be simple shapes so much.

Let's view simple shapes meeting in various syngonies.

In the lowest syngonies following simple shapes are possible.

Pedion - the simple shape presented by one facet.

Pinacoid - two equal parallel facets which can be back located.

Dihedral - two equal intercrossed facets (can be intercrossed on the continuation).

Trimetric prism - four equal in pairs parallel facets; in section form a rhombus.

Trimetric pyramid - four equal intercrossed facets; in section also form a rhombus.

The numbered simple shapes concern to unclosed as they do not close space. Presence at a crystal of open simple shapes, for example, a trimetric prism bindingly causes presence of other simple shapes, for example, a pinacoid or the trimetric dipyramid, necessary that the closed shape was gained.

From the closed simple shapes of the lowest syngonies we will score the following.

Trimetric dipyramid - two trimetric pyramids combined by the warrants; the shape has eight different facets, giving in traversal section a rhombus;

Trimetric tetrahedron - four facets closing space and having the shape of scalene delta circuits.

At medial syngonies from numbered above simple shapes there can be only a pedion and a pinacoid. Prisms and pyramids will be open simple shapes of medial syngonies.

In corresponding syngonies there can be trigonal, tetragonal and hexagonal prisms. There can be prisms with the doubled number of facets: ditrigonal, ditetragonal and dihexagonal. In the latter case all facets are equal, but identical corners between them alternate through one.

Dipyramids concern the closed shapes, scalenohedrons, trapezohedrons, a rhombohedron and a tetragonal tetrahedron.

Dipyramids can be trigonal, tetragonal and hexagonal or at doubling of number of facets - ditrigonal, ditetragonal and dihexagonal. Dipyramids are represented by two pyramids combined by the warrants.

1. Scalenohedron - the simple shape consisting of equal versatile delta circuits. Scalenohedrons meet only in trigonal and tetragonal syngonies.
2. The trapezohedron - reminds a dipyramid. Facets of this simple shape look like tetragons, and lateral edges do not lay in one plane. Trapezohedrons are possible only in three views of symmetry where there are planes of symmetry.
3. The rhombohedron consists of six facets in the form of rhombuses, cubic It extended or flattened on a diagonal reminds is possible only in trigonal and hexagonal syngonies.
4. The tetragonal tetrahedron represents four equal facets in the form of isosceles delta circuits.

In a cubic syngony there are 15 simple shapes, all of them closed. Simple shapes of the lowest and medial syngonies in a cubic syngony do not meet.

Cube (hexahedron) represents in pairs parallel six square facets. If each facet of a cube to exchange four triangular facets to be gained the simple shape which is termed a tetrahexahedron.

The octahedron represents plurality of eight in pairs parallel facets. If each facet of an octahedron is replaced by three facets (trisoctahedron) by quantity of the legs of these facets distinguish a trigonal trisoctahedron, a tetragonal trisoctahedron and a pentagonal trisoctahedron. At displacement of a facet of an octahedron by six facets we will gain a hexoctahedron consisting of 48 facets.

The tetrahedron of a cubic syngony consists of four equipotential delta circuits closing space.

If each facet of a tetrahedron to exchange three facets by analogy to an octahedron we will gain a trigonal tri tetrahedron and a pentagonal tri tetrahedron.

The rhombic dodecahedron represents the simple shape consisting of 12 facets in the form of rhombuses.

The pentagonal dodecahedron also consists of 12 facets, but the wrong pentagons having the shape.

Didodecahedron - the "doubled" dodecahedron, which each facet it is exchanged by two facets; consists of 24 facets.