: How do I convey that a relationship is platonic? I've been toying around with the idea of writing a novel. The story revolves around two characters, one male and one female, and the perspective

Simply tell the story. What need to explain your story.

A maxim of Nietzche may be technically useful here:

A woman may very well form a friendship with a man, but for this to
endure, it must be assisted by a little physical antipathy.

So, a reversal.

Rather than ask how will the reader believe in a truly 'just friends' relationship between a boy and a girl. Introduce, from the start, and matter of factly, the slight, physical antipathy.

If nobody can put into words why their friendship works, then you ought not to either. There is simply nothing to negate.

The only thing that remains is the story itself. If it is well crafted, the reader will get why their friendship works so well, which must by definition be seamless with the story, however divergent the characters may be.

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People will ship them regardless
If you spend some time around the web, especially on webcomics and/or fanfics, you will see that people tend to endorse relationships (a.k.a. ship) any two characters that are close enough. The webcomics El Goonish Shive illustrates that in one strip.
Regardless of their appeared differences or even distance, it will happen.
But in the following, I will try to explain some approaches that might emphasize the platonic part of their relationship. Whether or not it is cliché or cheesy, depends mostly on how you do it.
Let ship builders build
You might just simply ignore it. You mentioned that your story is not a love story. So let your characters live their story the best they can, and let the readers imagine whatever they want. As mentioned, some will ship them in any case. Maybe even more if you try to prevent it.
Furthermore, most friends don't spend an elaborate amount of time debating the nature of their relationship, regardless of the sexes and/or sexual preferences of those friends. Why should your characters care?
This is, for me, particularly valid if you write some adventure, fantasy, or science fiction. They have enough to cope with than worry about that. And any approach you would use to avoid it, would simply dilute your story and break your rhythm.
The cute neighbour
One way to make some romantic distance, is for the characters to discuss some other romantic interests.
I also see it as realistic. Friends do discuss those things. And you mention that they are very close (quasi exclusive) friends. So who better than the other to discuss a crush?
And if you want to avoid bringing a secondary character, you might make it by simply having the characters discuss that cute boy in the metro, whom they know nothing about and will never meet again.
If both characters are at ease with that discussion and supportive, it will indicate to the readers that they are not interested in each other.
Been there, done that
Another way to convey the current situation to the readers is to give them a specific reason for it. Maybe, they were in a romantic relationship before and it did not work. Maybe, they met in specific circumstances (like each other's ex's getting together). Maybe they grew up together and consider each other like brothers. There are many other ways to convey that there's an actual reason in the past their relationship does not get more intimate.
On that note, they may simply took a chance to discuss what each was looking for in that relationship and agreed that having a great friend was really was they were looking for.
Explore the swings
Another way to explicitely convey the platonic relationship, is to explore away from the stereotypical hetero-centered characters. Sexual orientations are many and various. Having one or another character non hetero would provide some hints to your readers. You can have your female character be strictly lesbian, for example. And be fully out about it.
And if you want to avoid the typical only gay guys can be friends with girls trope, you could make one of them ACE. It works the same way, but is more original. Note that a reverse trope (lesbian+straight) is much less explored.
Note that depending on the style of your story, and time of it, it might be expected to have some romance in it. Most people in their 20s are attracted to other people (ace being the exception). They might not be attracted to each other, but they would be with someone else. Life threatening adventures usually provide great distractions...
Let them justify themselves
One way to explicitely indicate the relationship is to have one or more of the character explain the nature of their relationship.
Depending on the writing style you're aiming for, one of the character might be thinking about it. But that has the drawback, that if their relationship is fully assumed from both side, there's little reasons for that train of thoughts. And on the contrary, it might indicate that that character is questioning the current situation.
But as your readers will tend to ship them, so will their friends. I have seen it in real life, even lived it: a girl and a guy being really close, and their own friends wondering if something more is happening. You could have one character being openly curious about it to one, or even both characters, at the same time. Imagine the following conversation:

" Yesterday, I went to hike with Bob, it was great."
"... I did not realise you spent that amount of time with him. Is there something going on, that I wasn't informed of?"
"What me and Bob? Oh no, we're best of friends, but no, nothing else. Why, are you interested?"

You can leave it at that point, or combine it with something else, like: "no, he's gay", "no, he's in love with someone else", etc. Depending on the importance this has for you, and how inquisitive that third person is.
You might even do that without involving the characters themselves, as

"no need to wait for Bob, he is having lunch with Alice."
"Again? That's like almost every day... Are they together?"
"Not even. I don't get it, but no, happy friends. Never thought he'd be like that."

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I agree with several other answers that readers will expect some romantic tension between the two, simply because we are so accustomed to two protagonists of opposite genders in the end finally finding each other, even if or especially if it is constantly being said that they are just friends.

The most effective and believable way that I've found so far is that they actually did cross that line in the past, found that it didn't work out and managed to go back to being friends. You can reveal this to the reader in flashbacks or by them joking about it.

This establishes the most clearly that the reader can stop waiting, because it already happened, and now the topic is off the table.

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That feels sloppy, and doesn't resonate very well, because that’s how you see it… so why would your readers not agree?

How could you possibly “show that they're just friends, rather than… directly summarizing how they feel…”

Did you notice that in real life, anything is acceptable because that’s the way real life is but in fiction, that simply isn’t true? I think for example of an actress with a scarred arm. In real life, she has a scarred arm. So what? In any role she plays, that will be seen in the same light as The Girl with the Dragon Tattoo… which title can’t be ignored - try to - even though it’s in no way relevant.

In fiction, either don’t mention it at all, or mention it in a way that the reader will feel comfortable with. If that means giving a specific explanation, give one. If not, just be sure about that.

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Disclaimer: If your goal is to keep your readers from shipping your characters, you are out of luck. Readers are going to try and pair them no matter what you do. The fact that Ron x Voldemort fanfics exist is proof enough of that. That said, there are numerous ways to demonstrate a platonic relationship.

Give the characters incompatible orientations

If your girl doesn't like boys, or your boy doesn't like girls, then most readers will deduce pretty quickly that they aren't going to fall into bed any time soon.

I know of at least on case where this was done. Carrie Vaughn made one of the characters in the Kitty Norville series gay to help define his relationship to the main character. She then proceeded to incorporate his orientation as an important part of who he is. This is important. It's okay to define a character's orientation in order to meet a plot point, but you must then seek to understand how the character's orientation has affected who they are and the life they have lived. You can't just tack it on and hope it sticks.

Have another character assume that they are in a romantic relationship

And when the third character mentions their assumption to one (or both) of the pair, let the pair's reaction do all the talking. (Bursting out laughing is generally a good indication of a platonic relationship).

This gives you a natural way to hang a lantern on the issue in the story without it feeling unnatural.

Have the pair discuss their romantic lives with each other

Who do you go to for romantic advice if not your best friend? If your pair is discussing together the people they are interested in romantic relationships with, then it should quickly become clear that each other are not on the list.

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You could have them discuss their current significant others/dates or lack thereof in a platonic way, just as you'd write two male or two female friends discussing it with each other.

Do it in a way that is clear that the interest is "how is my friend doing in this area" and not "is the coast clear for me?"

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They have different sets of talents, different world views, different ways of handling crises. Yet despite all that sets them apart, they're the best of friends.

Why are they the best of friends? One theory of "friendship" I find useful for writing is the idea of mutual benefit. This can be demonstrated, for example, in music: If you and I like the same kinds of new bands, then with two of us on the lookout for new bands, and sharing our finds with each other, then we both end up discovering approximately twice as much. Likewise, friends that share a mutual interest in fashion, sports, food, sci-fi movies, television shows, and other forms of (say non-sexual) entertainment will have moments to share, similar memories, and will enjoy each other's company because of it.

It is human nature that most entertainment experiences are massively more fun if experienced with another than experienced alone. In studies, people watching a standup act will laugh much more often sitting with a heretofore stranger than they will laugh sitting and watching alone.

This is not to say that friends are alike in every respect; they may differ on many topics, on politics, on entertainment. But they probably will NOT be "the best of friends" unless they share several likes and dislikes, and share a world view on several topics.

Opposites do not attract; they repel. It is difficult for an atheist to be best friends with bible-pounding evangelical. It is difficult to enjoy the company of another if you think their politics is wrong, their religion is wrong, all their preferred entertainment is infantile or boring.

To be the best of friends, your characters need enough to share that they can enjoy spending time together. If there are topics to avoid, that must be possible without diminishing the time they spend together.

It is true that mutual benefit can arise from frequently used complementary skills, so that when we combine them we create something more valuable to both of us. Perhaps even something commercial: He is an artist, she is a writer, together they have a best-selling comic book, or they are best-sellers in the field of illustrated children's books.

(That is a hook to explain a platonic relationship despite a lot in common).

Otherwise I cannot see how you show them being the best of friends.

Nobody, including the two of them, can quite put into words why their friendship works as well as it does, but they're nonetheless inseparable.

I am guessing from this that you will just TELL us their friendship works and they are inseparable; because you can't figure out how to do it either, after making them polar opposites. The reason "nobody can put it into words" (including the author) is because it makes no sense!

You need something to stop people that are plausibly best friends from becoming lovers. A deal breaking disagreement or pre-existing condition. This can be something discussed once or mentioned off-hand, and a topic they avoid talking about.

One such might be religion; neither will marry outside their different faiths.

Another might be their mutual business: A refusal to mix business and love life, and perhaps ruin both.

Another might be a shared history: Raised in the same foster home; and they feel like brother and sister, even if not blood-related.

Another might be blood relation: They are cousins, and not kissing cousins. Or children of the same "wandering" father but different mothers, raised separately and discovered each other later.

Another might be a significant age difference; typically romantic interests are not visibly older than each other.

I could directly call out the fact that they don't view each other in a romantic light, but that feels sloppy, and doesn't resonate very well.

It feels sloppy and doesn't resonate because it is just telling, with no plausible reason. I could not write this relationship without SOME plausible reason for them avoiding romance. The notion that a normal heterosexual male and a normal heterosexual female that are the best of friends, unattached, for a long time both never ever consider each other as a love interest is simply not plausible. You could make one or both of them have rather improbable personality issues; homosexuality or extreme intimacy or sexual aversion, but then you will have given a reason!

Normal adults want romantic connections, and friendship is often the first step in that direction; failing to take the next step demands a reason you must supply. IMO, "Because author tells us so" will just make people put down the story, for not making sense.

So although I might be surprised by your skill in pulling this off, I think for myself your constraints would make this impossible to write as anything I would regard as good work.

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Readers expected my protagonists to fall in love when they meet. Maybe I did too, but I knew it was a cliche and didn't want it. It turned out as I wrote that the male character had sparks with a secondary character, who he met before he met the female protagonist.

I've learned that the way to telegraph attraction most strongly, in addition to the dialog, is what he notices. He notices how she smells. He notices that her hair is done differently. Et cetera. He thinks things like 'WHy should I care if she doesn't notice me?'

When he meets the female protagonist there were no sparks. I wanted it platonic. He doesn't notice her hair. He doesn't notice much about her. But when he does, it's neutral (and it leans toward unflattering). She's short. She looks like a kid. Her shoes are clunky. He doesn't give any thought at all to whether she thinks about him.

She, conversely, doesn't think about him. She doesn't notice that he's tall, or exotic - because he's such a fish out of water that it's more obvious to her that he just - isn't at all helpful to what she needs (her goal). No sparks.

They become friends through shared purpose.

Would this series of relationships work if he hadn't met the secondary character first? I don't know. I do know the readers expected the two protagonists to fall in love in the beginning of the book. And that when he meets the secondary character first, they expect him to like her. (oddly, they don't care what she thinks, but that may be a PoV issue.)

Answer: I think you communicate it through what he notices about this girl, and what she notices about him. They don't notice anything remotely physically attractive. They notice the other things.

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Why not let one of them, or both, have their own love interests?

Or let them fight over a common love interest.

The last one in particular could establish just how great they are as friends, that not even jealousy could break their friendship.

Another idea could be to let them briefly believe that they are in love with each other, but through that experience show just how unfit they are in a romantic relationship and let it resolve into a perhaps even stronger platonic relationship.

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You could have another character address the issue.

For example, have one character ask "You two get on so well together, how come you're not together?" and then have one or both of the characters address the issue directly, with something like "It just wouldn't work." or "We get on, but there's no attraction/spark.".

That way you've brought it to light and dismissed the idea in an unambiguous and believable way, in your character's own words.

As @Fayth85 says, there will always be people who expect romance no matter what you do, partly because they're either seeking it (even when it isn't there), perhaps because it's one of their main reasons for reading, or simply because it's become such a trope that nearly every story under the sun has romance shoe-horned into it at some point, no matter what the genre or intent.

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Well. There are ways to handle this. The simplest is never address it. They're friends, they get along, and they work well together. People may/will ship them, but that isn't how you wrote them.

People will ship (slang term, meaning to imagine them in a relationship) them whether you specifically, unequivocally state they are just friends.

People will ship them if you say he's gay and she's a lesbian.

There's nothing you can do that will cause people to see them as the best of friends and that's it. Even if, at the end of the story, they're married to other people, have kids, and are still acting the same way they are at the beginning. They'll just 'assume' they haven't come to terms with it; even if they're in their nineties and are still best friends and still completely platonic.

People ship characters, even when they don't make sense but it reminds them of a cute couple (i.e. themselves with their idealized partner). There's no stopping that. So write them as they are and address it or don't. People will ship them anyway.

Examples. Sasuke and Naruto, from the series Naruto. People still ship them, even though they are married to women and have kids.

Sam and Frodo, from Lord of the Rings.

Black Widow and practically every man she's ever spoken with in the MCU.

From Pacific Rim, the two leads. Not romantically involved. I haven't even seen the movie, and I know this because of the shipping is so on that its wake slapped me awake. (Too many relationship critique YouTube video talks about this particular pairing, because they weren't romantically involved)

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I agree that establishing the platonic nature of the relationship is important. There are a number of ways to approach it, as in David Doyle's answer.

But additionally, I wanted to point out a couple key things to consider:

Be aware that even if you gently indicate that the relationship is platonic, many readers will still be watching for signs that there's a potential relationship waiting to blossom. That is the nature of literature - many of humanity's stories revolve around a romance story or contain one, thus readers will have a strong tendency to suspect romance. They may even start to hold out hope.

Therefore, if you don't want that tension to develop and the reader's hopes end up unfulfilled, it's probably best to establish a clear reason why it isn't romantic and never will become one. There are numerous non-cheesy ways to say that someone loves someone like a sibling.

Secondly, in your question you state "not something they've ever considered," when perhaps that is part of the problem you're running into. The "romantic feelings haven't ever been considered" scenario is actually at the root of numerous love stories: "when X pauses to truly consider his feelings for Y for the first time, he finally realizes his love for her." It's almost a trope.

But if instead they have considered it, and then come to a clear conclusion that they have no romantic interests for a good reason, it is going to be more plausible that a romance isn't likely to develop. Then readers will be less tempted to draw romantic tension into it.

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The best way to illuminate a boundary is to cross it. Barring that, the second best way is almost cross it.

Have your characters accomplish some major task together, despite long odds. Then, as they are celebrating that small victory, have them catch each others eyes. Hold them there, teetering on the brink of it becoming something greater, then in perfect synchronization, as if sharing a well established joke, have them smile with mischief shining from their eyes. Both confident in the support and loyalty of the other. Both thrilled with what together they have accomplished. Both knowing that their current lifelong bond is better than the steamy short-lived alternative which awaits them down the alternative path.

You don't have to say any of it. Just make sure to show that each is happy in the now and untroubled by their aborted brush with intimacy. Romantics will always hope that this will change, but if the friendship is unfailing and supportive in both directions, it will fill the "better than real life" fantasy that your readers crave, without getting all mushy.

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I feel like the best way to say that they are friends is to make a comparison. That might just be me, but without directly expressing that they will never have feelings for each other, what you want to do is maybe have one of the characters compare them to an everlasting friendship, such as Twain and Tesla, for example. And maybe have another one of them explain the real reasoning behind the fact they will never have feelings for each other. At some point, you will have to express that.

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