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Is it enough to generally say that an object is (or is not) chiral in some space/some number of dimensions according to some convention, or is some sort of structure or description of how it is chiral usually recommended/required (at least implicitly by context)? In other words, in order to fully describe the state of being chiral, what features must be referenced?

Andrés E. Caicedo
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kevin
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1 Answers1

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Chiral is a term coming from the greek word $\chi\epsilon\iota\rho$, which means "hand". In fact, your hands are chiral in the sense of a sort of mirror simmetry between them.

I'd say that the term on its own is not really precise, it is as ambiguous as the term symmetric. There are some contexts in which it can be used freely (in chemistry, for example, chirality is a concept that needs not further specifications), but even in these contexts the state of chirality has a precise technical meaning (which may be implicit or introduced as a definition and then summarized by the term itself).

Franco
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    Mappings $f:\mathbb{R}^n \to \mathbb{R}^n$ are congruences or isometries if and only if they are of the form $f(x)=Ax+b$ where $A$ is an orthogonal $n\times n$ matrix, and $b$ is a translation vector. Then I would say a subset $S\subseteq\mathbb{R}^n$ is achiral is there exists some orientation-reversing isometry $f$ (i.e. $f(x)=Ax+b$ and the determinant of $A$ is negative) such that $f(S)=S$. If no such mapping exists, i.e. if $f$ is necessarily orientation-preserving (a rigid motion), then $S$ is chiral. – Jeppe Stig Nielsen Apr 15 '14 at 08:41