n. An object, animate or inanimate, standing for or representing something moral or intellectual; anything which typifies an idea or a quality; a representation; a figure; an emblem; a type: as, the lion is the symbol of courage, the lamb of meekness or patience, the olive-branch of peace, and the scepter of power.n. A letter or character which is significant; a mark which stands for something; a sign, as the letters and marks representing objects, elements, or operations in chemistry, mathematics, astronomy, etc.n. That which specially distinguishes one regarded in a particular character or as occupying a particular office; an object or a figure typifying an individuality; an attribute: as, a trident is the symbol of Neptune, the peacock of Juno, a mirror or an apple of Venus.n. In theology, a summary of religious doctrine accepted as an authoritative and official statement of the belief of the Christian church or of one of its denominations; a Christian creed.n. In mathematics, an algebraical sign of any object or operation. See notation, 2.n. In numismatics, a small device in the field of a coin.To symbolize.n. A contribution to a common meal or entertainment; share; lot; portion.n. In crystallography, the symbol of a face is the mathematical expression defining its position with reference to the assumed crystallographic axes. The symbols of Weiss (1818) consist of the in tercepts on the axes written out in full, as a : nb:mc for the general case, the fundamental axial values being designated by a and b (lateral), and c (vertical): thus a:b: ∞ cand a : b :3c are special examples. The Naumann symbols (1830) are adapted from those of Weiss; the expression is abbreviated, the order is inverted, and certain distinguishing signs are added. For the examples given, Naumann's symbols are: general case, m Pn (also mPñ. mPn, etc) or mOn (for the isometric system); further ∞ . The Dana symbols (1850) are those of Naumann further abbreviated, as m-n (m-ñ, m-n etc), etc. In the Millerian system, now generally adopted (introduced by W H. Miller of Cambridge in 1852). the symbol consists of three indexes, which are either whole numbers or zero. For the general case, the symbol is hkl and the relation of the indexes h, k, and l to the axial intercepts is given by the full expression this last can be derived from the symbol ot Weiss if the coefficients are reduced to fractions having unity as their numerators. The Miller symbols for the special examples given above are 320, 321. Bravais (1866) suggested extending the Millerian system to hexagonal forms referred to four crystallographic axes; hence the Bravais-Miller symbols have theform (general), , , etc. When the indexes are included in brackets or parentheses, as [321], (321), this expression is generally understood to be the symbol of the form — that is, to include all the faces which belong to it; thus the orthorhombic form (321) or (321) includes the eight faces , : here as always in the Millerian system negative values are indicated by a sign placed over the index. The zone-symbol, from which the common relation of the indexes for all forns lying in the zone is deduced, is similar to that of a crystal form but is usually inclosed in square brackets: thus the zone-symbol [11ī] means that for every face in the given zone the zonal equation h + k = l holds good.—Identity symbol. See identity.