In other sections, two related problems are discussed:

How are homonymy and polysemy distinguished in the structure of the lexical database?
How are homonymy and polysemy distinguished in the structure of the dictionary?

Here we look more closely at the internal structure of a polysemous entry in a print dictionary.

Bilingual dictionary

In a bilingual dictionary, polysemy plays different roles in the two volumes:

As explained elsewhere, the L₁–L₂ volume serves the user in an onomasiological perspective. If it took that perspective consistently, L₁ polysemy would not come up. Due to its reliance on L₁ and its usual alphabetical order, however, the lemmas constituting entries are not concepts, but L₁ words, and these may be polysemous. The first task of a polysemous entry in an L₁–L₂ dictionary is therefore to orient the user towards that specific meaning of the L₁ lemma that he wishes to express.
The L₂–L₁ volume of a bilingual dictionary takes a semasiological perspective. If the expression for which the user opens the dictionary is polysemous, then the dictionary must help him in disambiguating it. The task of the entry is then to guide the user to the particular sense of the lemma by means of its structural properties.

Monolingual dictionary

In an onomasiological perspective, polysemy is not even seen. Consequently, it plays no role in an onomasiological dictionary.

The general monolingual dictionary is a semasiological dictionary as far as the access via an alphabetical macrostructure is concerned. However, dictionary makers often do not tie themselves down to one or the other alternative. As a consequence, one finds the monolingual counterpart of both of the above-mentioned approaches of the bilingual dictionary:

In the onomasiological approach, polysemous items are subdivided by semantic criteria. The senses may then be ordered by one of two principles:

In a synchronic perspective, first the generic meaning (German Gesamtbedeutung) is given, including metaphorical extensions; then follow the various specifications and metonymies. The advantage of this approach is its systematicity; the disadvantage is that the generic meaning may be highly abstract.
- In ordering the senses, frequency may be considered. Although this could, in principle, be observed exclusively, in practice it never is. It is, however, often used in an intuitive way to order the various specifications and to cut the enumeration off at some point of low frequency.
In a diachronic perspective, first the basic meaning (German Grundbedeutung) is given, then follow the various extensions and metaphors, narrowings and metonymies, in chronological order. The advantage of this approach is that it can usually rely on a concrete concept, which renders intuitive access to the meaning easier. Its disadvantage is that it gives or presupposes historical information, which is proper of an etymological dictionary and may be irrelevant for use in synchrony.

In the semasiological approach, polysemous items are subdivided by structural criteria. These are essentially distributional in nature, i.e. they rely on morphological or syntactic constructions that the item enters and on specific items, or classes of items, that appear in its context.
In this approach, the primary order criterion of the microstructure are variants of the lemma according to grammatical subcategories. For instance, the entry of a verb is first subdivided according to valency (intransitive vs. transitive vs. reflexive construction), then according to the preposition governed or, for particle verbs, according to the adverb complementing the verb root.

Order of senses in print

As to the typographic layout of senses, there are two decisions to be made:

At the level of the macrostructure, a sense of a polysemous item may be hypostatized to an entry of its own, or it may be a subentry of a generic entry.
If the latter, then the nesting microstructure of the complex entry may be linear or hierarchical.

As for #1, there is a lowest level of differentiation which is always done within the simple entry and even within one sense specification. For instance, in a German-English dictionary, one never finds:

¹Basis base
²Basis basis
³Basis basement

and instead one always finds

Basis base, basis, basement

The question is therefore what magnitude of difference among the senses of a word justifies setting up different entries. Again, there are semantic and structural criteria:

Above the dividing line between homonymy and polysemy, i.e. for lemmas considered semantically disjunct, independent entries are normally set up and distinguished by homonym number.
If the lemma is found in different syntactic categories (it is heterosemous), then that may be sufficient reason to list it in independent entries, even if these are related by a regular conversion relation.

By criterion #b, an English dictionary has:

¹peel n skin or rind
²peel v strip the skin or rind from

As for alternative #2 above, there is usually at least a two-level hierarchy of semantic distances. The upper level is reserved for distinct senses, the lower level for alternative paraphrases or – in a bilingual dictionary – meaning equivalents which individually or jointly serve to characterize the specific sense in question. For instance, my English dictionary features:

wild adj ... 3: waste, desolate (~ country) 4: uncontrolled, unrestrained, unruly (~ passions) ...

Here #3 and #4 are distinct senses, while ‘waste’ and ‘desolate’ both characterize sense #3.

In a bilingual dictionary, this kind of hierarchy is commonly brought out by indicating the distinctive criterion at the beginning of a sense. For instance, my English-German dictionary has:

wind tr.v winden, (auf)wickeln; mar steuern ...; (Horn) blasen ...

Here two disparate criteria are used for differentiation: mar refers to a special language, while ‘Horn’ identifies a sense by a selection restriction. (The difference in kind of the two criteria is signalled typographically.) This is, incidentally, one of the rare cases where obvious homonyms are described in a single entry.

As the examples show, the conventional strength of punctuation marks (‘.’ > ‘;’ > ‘,’) is commonly made use of in showing hierarchical steps. A dictionary may abide by that device, or it may number the senses at the highest level, and it may even bring out almost any number of hierarchical levels by making use of ‘1, 2, ...’, ‘a, b, ...’ ‘i, ii, ...’, ‘α, β, ...’ and so forth, as is done in the Thesaurus Linguae Latinae. It is probably wise to steer a middle course here. At any rate, a pure one-level enumeration is unable to bring out semantic relatedness.

References

Hausmann 1977, ch. 3, Sinclair ch. 3