Does anyone know a visual sign that is an icon, an index and a symbol at the same time for all speakers in one community? I thought of the visual sign of a dove, but I'm afraid it is not an index. Thank you very much!
This sounds like you're asking for help with homework. But it's perhaps an important issue to address, so here it goes:
The very way the question is formulated shows how confused and pointless this tripartite typology of sign is.
You ask about something being both icon, index and symbol for a community of speakers. But, of course, something being a sign for something in a community of speakers is the very definition of symbol which describes a situation where the signifier (vehicle) is related to the signified (object) through convention. So if something is an icon or index, it should be related by virtue of similarity of contiguity. But we know that all such relationships are conventional and do not hold across cultures. So every possible example of an icon (arrows, maps, images) or an index (symptoms, parts) is also symbolic. But for something to be both an icon and an index is a contradiction in terms.
Of course, many signifiers are both symbols, icons and indexes but not in relation to the same signified. For instance, smoke is an index in relation to fire, icon in relation to itself (e.g. in a picture of smoke) and symbol if used to communicate some preagreed meaning. But that does not seem to be what you're asking.
However, all of this does not help us solve any interesting or useful problems in semantics. It's a classification that's at best of interest to itself. The only important part is the question about symbolic communication (ie about convention) which is why I believe Roman Jakobson brought this to the attention of linguistics. However, ever since it's been treated as some sort of taxonomy on par with Linnean classifications which it is not.
It is much more useful to talk about the range of motivation for the relationship between the signigier and signified (if we even want to talk in such terms). Because, there are many more motivations that enter this relationship than can be captured by such simplistic division. Just think about the fine grained complexity behind the attempted renaming of French to Freedom fries. Or the more common and successful renaming of government departments or academic disciplines. Those are all symbolic but a result of a range of motivations that include those of iconicity (similarity) and indexicality (contiguity) but also so much more (narratives, categorisations, scenarios, etc.) (See Lakoff, Women, Fire and Dangerous Things for an interesting elaboration of this. Ch. 4 and 5 in particular.) Any simplistic and fixed classification like this one can only get in the way. It is the sort of things linguistics textbook authors and teachers of intro courses revel in but that's more useful as an exam question than a real analytic category.