Homestuck: On Alternia, trolls are biologically hardwired to form love dodecahedrons (they pool genetic material and another species incubates it). As Karkat puts it, "FOUR IS PRETTY MUCH THE MINIMUM VALUE FOR LOVE-HATE N-DRANGLES." They have four types of romance, divided into quadrants depending on whether they are red (compassionate) or black (hateful), and concupiscent or conciliatory (pseudo-platonic). Matespritship ( ♥) is the closest to the human concept of romantic love; kismesissitude (♠) is passionate, carnal hatred; moirallegiance ( ♦) is close-knitfriendship functioning as someone's better half; and auspisticism (♣) is a three-way relationship in which a mediator prevents two trolls from escalating into kismeses. Trolls are urged to secure mates in every quadrant, which means things can quickly get chaotic and confusing for everyone involved.
A volatile love dodecahedron is illustrated in the story itself: Eridan wants to be matesprits with Feferi, but he's been moirail-zoned. Likewise, Kanaya is Vriska's moirail, but she wants a matespritship. Vriska is attracted to Tavros and ready and willing to be his kismesis or his matesprit, but he can't return her hatred and he's too scared of her for the latter. Kanaya is their auspistice, and mediates between Vriska and Eridan as well, who have a potential kismesissitude. (And on top of all that, quite a few shippers are sure that Feferi and Tavros would be perfect together.) Phew!
Oh, but there's more. Feferi now seems to be the matesprit or moirail of Sollux, who used to be one of the two with Aradia. Aradia is now quadrant vacillating (read: alternately ♥ and ♠) with Equius, who is Nepeta's moirail. Nepeta has a ♥ crush on Karkat, who both has a thing with Terezi (who might be ♠ for Vriska) and once believed John to be his kismesis. This means that out of all the trolls, Gamzee is the only one not romantically involved. Canonically, anyway.
As of the September hiatus, Gamzee is flushed for Tavros and in an official moirallegiance with Karkat.
This gets even more confusing now, and when you put into account the Earth Kids, as detailed in this image◊.
Karkat had a hatecrush on John, and pre-Cascade pesterlogs indicate that he might have been developing flushed feelings for Jade. Meanwhile, Karkat also believes that Vriska is crushing on John, though John is unsure about this when Karkat tells him, and Terezi has been acting rather flirtatiously towards Dave, though when questioned on the subject by Rose, Dave responded that his and Terezi's relationship was nothing more than an "interspecies partnership in incredibly shitty cartooning."
And then there's more: Eridan kills Feferi and Kanaya, ruining Sollux's relationship. Gamzee goes nuts and kills Equius and Nepeta, and Vriska offs Tavros for maturing far too late for Vriska's liking. Kanaya comes back as a vampire and beats up Gamzee and Vriska, then kills Eridan. Vriska now has crush on Kanaya while Feferi, Equius, Nepeta and Tavros are dead. Then Tavros was hanging with a dead Dave and an Aradia while all the dead trolls and kids visit each other's bubbles, possibly upturning every canon ship ever.
But Wait, There's More!. Gamzee is implied to have went nuts due to seeing the dead body of Tavros, whom he was flushed for. John and Vriska both apparently have crushes on each other but Vriska is killed by Terezi before John could make anything out of it, but Karkat never informs John that she's dead. Jade kisses Dave and John kisses Rose in order to revive them. Karkat and Terezi appear to still have flushed feelings for each other.
Then, after Cascade, there's also the Alpha timeline where all of the kids have a crush on Jake - including Dirk. Later Jane attempts to admit her feelings to Jake (who also had feelings for Jane) and fails and leads Jake into thinking they are Just Friends and decides that he might take action on his feelings for Dirk. To add to that, Jake also develops feelings for Aranea, Vriska's ancestor from pre-Scratch Alternia.
And that's not all! Karkat admits he's flushed for Terezi, while future!Karkat pooints out that he's been hateflirting with her too. He's also worried Terezi and Dave may have a thing going on. As a result, Karkat tried to get Dave into a quadrant vacillation with Terezi in sync with his own vacillation with her, which ended up with Karkat seemingly developing black feelings for Dave. Dave also called Roxy a "choice babe" without knowledge that that was his mom, and fans are debating whether Kanaya's hatred of Gamzee is platonic or not.
It keeps happening! Meenah starts to get a crush on Karkat and inadvertently ends up scaring away Terezi, who might have been about to confess to Karkat as well. Meenah also has acted arguably flirtily with Aranea at some points. Meanwhile, Latula and Mituna have been in a happy relationship for a while, but there has been some UST between Latula and Kankri. Kankri has a familial-esque relationship with Porrim, who is implied to have been in a relationship with Latula briefly (as well as most of the pre-scratch trolls, including Aranea). Mituna also used to be in a moirallegiance with Kurloz who used to be in a red relationship with Meulin, although the latter two are just friends now. Sort of. And then there's Cronus who tries unsuccessfully, and quite douchily, to hit on everyone but inevitably fails. Also, Jade and Davesprite dated for a while but then broke up, while Rose and Kanaya seem to be going out.[[/labelnote
I warned you about Love Dodecahedrons bro! [[labelnote:==>]]Tavros and Vriska are a couple in the afterlife and John is fairly jealous about it. Roxy has feelings for both Jane and Dirk, and confessed her love for Dirk in trickster mode. Dirk kisses Roxy to stop her from making advances on him. Dirk and Jake broke up due to communication issues but Jake possibly still has feelings for him. Jane, Jake, Roxy and Dirk get four way married when they were in trickster mode. Jane confessed her love to Jake who recuperated, except they weren't in the right frame of mind at the time.]]
Just to complicate things even further, not only does Homestuck accommodate multiple kinds of romance, but also multiple versions of the same person in different timelines, universes, or alternate realities. So while Mom and Dad were in a relationship in the pre-scratch human universe, in the post-scratch universe Mom's alternate self, Roxy, is the same age as Dad's daughter, Jane, and only thinks of him as kinda hot. This leads to a situation in which the whole John/Vriska thing was apparently resolved when Vriska dies and John claims he was never into her, only for it later to turn out that dead!Vriska briefly dated the dead John from the doomed alternate timeline before breaking up with him and dating dead!Tavros instead.
Anyone trying to pursue a black relationship with Karkat will also have to deal with the fact that Karkat comprises a complete black romance dodecahedron all by himself; any two versions of Karkat who have interacted with each other, whether they are from alternate timelines or from fifteen minutes apart in the same timeline, have immediately developed a deep mutual contempt. At one point, Nepeta starts shipping Jade ♣ Karkat and Karkat.
John is Genre Savvy enough to have sworn off romance, at least for the duration of the game. This doesn't stop him from getting a ton of Ship Tease, as seen above. In Act 6, he gets even more ship teasing with Roxy.
Bittersweet Candy Bowl's central story is about a love dodecahedron. Mike, a dogged good guy, and Lucy, a tsundre, seem to be destined for each other at the start of the comic, but over time the pair drift apart as Mike finally acknowledges that he is in a Long-Distance Relationship with his love from third grade. Mike is a handsome cat, and Daisy, his best female friend other than Lucy, pursues HIM doggedly, while she herself is being pursued by the aloof Augustus and the dogged stalker/white knight Abbey, with Paulo, her best male friend, possibly being interested in her as well, though this is less than clear and if it is so, she is quite oblivious to it. Meanwhile Lucy for her part shares a crush with Paulo, a confident jerk with a heart of gold, but he feels that he would just mess her up further. Several other friends fancy Lucy, including David, a dog who she is completely uninterested in, and Jessica, who is bisexual. Paulo himself is at the center of several female's attention, including his almost girlfriend Tess, an older girl who does not want to commit to a relationship with him despite the two being in love with each other, Rachel, who, being a dog, cannot stay with him if she wants kids, and Jasmine, a younger girl who looks up to him. Further complicating matters, Paulo slept with both Jessica and Rachel, who are Tess's archenemies, and little did he realize at the time, but the pair did it to get back at Tess for wronging them two years ago. The comic creator, Taeshi, actually sells a relationship chart poster in her store.
Yuki was a schoolgirl with a crush on Piro. She seems to be getting over the crush, but now Miho is taking her under her wing, and she seems to have acquired a boyfriend by falling on him and breaking his leg.
In El Goonish Shive, a rather surreal love dodecahedron is played for both laughs and drama, but has been resolved so that four of the six involved are now in relationships: Elliot with Sarah, and Nanase with Ellen, though whether or not one of those characters (Ellen) qualifies as being in the Dodecahedron is complicated, due to Cloning Blues being involved. Clever way to have Nanase's Loving a Shadow with Elliot end in her finding someone perfect for her, though. The last one, gay Justin, has given up on straight Elliot, and wound up stuck in I Want My Beloved to Be Happy land. Melissa, attached to the Dodecahedron via Justin, doesn't get that he's gay, while Susan, whose Kindred Spirit relationship with Justin is revealed essentially the moment they meet, apparently has some feelings for him but knows she can't pursue them. For a brief period after her splitting off from Elliot, Ellen displayed feelings towards Sarah, though it's implied that she's over it.
When you throw magical transformations into the mix it gets even more complex. Elliot's got a spell that can turn him into a superhero and one of three girls (for secret identities), and the shy one has a crush on Justin. Dan, you are cruel.
It can get more complicated. While Nanase and Ellen are dating, Ellen shows at least some attraction to Tedd (going as far as admitting that he is sexy and confusing), both Catalina and Matt Cohen asked Susan out on a date, Catalina is currently dating Rhoda, and Melissa has a friends-with-benefits situation with Noah. If you include subtext, Rhoda shows signs of interest in Diane, the prevailing opinion is that Justin's coworker George has a crush on him, Noah gushes over both Grace and Elliot (though there are non-romantic reasons for this), and Susan seems to be attracted to Elliot, of all people. Not exactly something out of place in a high school.
The current situation may well be too complicated to explain without a diagram, but here goes: Elliot, who used to date both Nanase (who is gay and now dating his sister/opposite-sex-clone Ellen) and Sarah, but is still good friends with both of them, is now dating Ashley (who is bisexual), but also has feelings for Susan, who returns them but can't do anything about it. Susan also once had a crush on Justin, (and made out with him once when they were both genderswapped), and has a long lost half-sister she is unaware of in Diane, who also likes Elliot. Diane has a woman-crush on Nanase, and her friend Rhoda has an actual crush on her, but is dating Catalina, who has a crush on Susan. Meanwhile Justin is also in love with Elliot, but has recently asked out Luke, after finally having it out with his old friend Melissa who had harbored feelings for him while refusing to acknowledge his sexuality, and who is now dating Noah, who may or may not have a man-crush on Elliot and who definitely practically worships Grace, who is in love with and dating Tedd, who is cousins with Nanase and heterosexual life partners with Elliot. Whew.
Avalon: Ceilidh and Joe are the Official Couple, but Joe is primarily interested in Helène, the girlfriend of Alan (who would much rather be with Ceilidh), and secondarily interested in Phoebe, who, if she likes anyone, likes Ceilidh; Ryan and Iain are also interested in Phoebe. Ceilidh herself isn't sure whether she likes Joe, Iain, or Phoebe... but definitely not Alan.
Implied in thisxkcd comic (though strictly speaking it could just be a cycle or even a collection of disconnected relationships).
Arthur, King of Time and Space, or at least the Space Arc where everyone is crammed into the same spaceship, is heading in that direction, mostly using canonical relationships. Arthur loves Guinevere but has a child with Morgan. Guinevere loves Arthur and Lancelot. Lancelot loves Guinevere but has a child with Elaine of Carbonek. Galehaut loves Lancelot. It's still relatively easy to follow, but the comic is meant to last twenty-five years...
Therapist: Hang on, hang on. I'm gonna get some thumbtacks and colored strings so we can diagram this.
The apparently complicated lesbian dodecahedron at the university.
Girl Genius is somewhat unusual in that the most complex love dodecahedron belongs not to the protagonists but to the minions. Moloch von Zinzer has had a crush on Sanaa Wilhelm aka Sanaa Tryggvassen for a while, which is obvious to just about everyone - Sanaa thinks he's hopeless, and is embarrassed and fairly contemptuous. Violetta comes into the picture after a while and gets on fairly well with von Zinzer as friends, then starts developing feelings - it's not known whether he knows about that. Fraulein Snaug then turns up, decides she quite likes von Zinzer, and asks Violetta if they're dating. She takes Violetta's negative answer as permission to pursue von Zinzer with unreasonable enthusiasm, which he seems to be a little uncomfortable with at times - although this could just be down to the fact that she keeps insisting he'd be the best Chief Minion ever, which is his idea of a nightmare. Then von Zinzer suddenly becomes much more competent than he was before, mainly because of his extreme genre savvy-ness and Sanaa suddenly decides that dating him wouldn't be so bad after all. Von Zinzer is basically clueless of everything happening, up to and including the obvious flirting.
von Zinzer:[to a fuming Snaug after Sanaa started flirting with him] I mean, I still like her, but see - until these last few days, I never had a chance to get used to being around attractive women! So, Sanaa? Yeah, she's smart and tough and I like being around her - but since I feel the same way about you, I obviously don't know anything about romance. Stupid, huh?
The situation with Agatha as the protagonist is less complex - her initial love interest was Gil, which was temporarily put on hold when his father tried to capture or kill her. She had a potential relationship with Lars, but that didn't end so well. Currently it's more of a Love Triangle with Gil and Tarvek, but ventures into dodecahedron territory with the addition of Xerxsephnia von Blitzengaard, who is trying to persuade Gil into a sensible political marriage and also holds feelings for him, and Martellus von Blitzengaard, who has no feelings for Agatha whatsoever but still wants to marry her just for the prestige and control. To make matters worse, the von Blitzengaards are both Tarvek's cousins and want him dead, or at least out the way, and Martellus also wants to kill Gil.
Gunnerkrigg Court has slowly revealed that the prior generation is a surprising tangle of former couples and unrequited love. By contrast, all the pairings among Annie's generation are pretty straightforward (even if the exact nature of their relationship isn't).
Star Guys has a wonderful one: Jupiter likes Venus, who likes Jupiter back (but neither know), Centauri also likes Venus and wants her back, but Venus is oblivious to him. Meanwhile, Saturn likes Mercury, who likes Neptune, while Earth and Orceus like Ana, who's asexual, and hates Earth. Finally, Pluto likes Mars (who may or may not like him back), whilst Jeeves likes Pluto, despite him stating that he's gay.
All of the major characters in Out There, with the notable exception of John, have at one time or another been infatuated with at least one of the other major characters. Miriam, as the main character, has dated, had flings with, or been otherwise at least temporarily fascinated with no less than 8 major characters: John (unrequited love/lust), Wally (fling, as part of the back story), Chuck ("officially" dated), Clayton (aborted fling), Sherry (unconfirmed, but strongly implied, past fling and/or relationship), Rod (fling), Steven ("officially" dated), and Araceli (infatuation); this doesn't even cover the list of characters (most of them minor or non-recurring characters) who have been at least temporarily captivated by her. While Miriam holds the record in all love/lust categories, Sherry's list is almost as impressive (embarrassing?): Steven (dated, as part of the back story), John (brief, and relatively mild, infatuation during a short period of essentially platonic dating), Chuck (big-time crush, finally culminating in an "official" relationship that is ongoing), Rod (brief interest until he "blew it"), Clayton (one-sided—he wants her, she's repulsed), Araceli (one-sided—Sherry is clueless about Ari's infatuation), and Miriam (unconfirmed).Out There is unabashedly a soap opera.
Ménage à 3: You'll need a wall chart. A big one. See the notes on the comic's own page, which can at least try to keep up with the madhouse; there's little point in duplicating them here. Let's just say that the joke in a guest strip about everyone in Montreal having sex with everyone else looks less excessive by the month.
In Eons Ago, Starscream has Megatron, Soundwave and Steve the Vehicon in love with him, and in the past he had to deal with the affections of his friend Skyfire and his fiance Steelmind, the latter of whom had to deal with Shockwave's affections. It gets a little more complicated, considering Soundwave and Steve are the reincarnations (so to speak) of Steelmind and Skyfire, respectively.