Anime / Lagrange: The Flower of Rin-ne

Left to right: Muginami, Madoka, and Lan.

Lagrange: The Flower of Rin-ne (輪廻のラグランジェ Flower declaration of your heart, Rinne no Raguranje) is a mecha anime produced by Production I.G. The first season aired during the Winter 2012 anime season and the second during the Summer season of that same year. Each season is twelve episodes long. Two OVAs were made, one called "Kamogawa Days", which acts as something of an epilogue to the first season, and "Kamogawa Memoria", which is a recap. Twelve, three-minute long specials were included between the two seasons' Bluray/DVD releases.

Madoka Kyouno is the sole member of the Jersey Club, a school club dedicated to helping people. The seaside town of Kamogawa gives Madoka plenty of opportunities, and she's always prepared to lend a hand. Or even save a life, which is what happens one day when she rescues a mysterious silver-haired girl from drowning. The girl turns out to actually be an alien princess nicknamed Lan.

Lan wants Madoka to pilot an Ovid, a robotic aircraft that can transform from an airplane into a bipedal mecha. Despite only learning about them that day, Madoka has vague memories regarding one specific Ovid, the green Vox Aura. Lan herself is connected to the blue Vox Lympha and another alien girl called Muginami is bonded to the orange Vox Ignis.

The three of them work together with the military organization Nuvomundos to combat the members of the alien organization of Kiss. Kiss's leader, Lord Villagulio from the planet De Metrio, wants to get his hands on the Vox Units so he can destroy the Polyhedron Federation and their planet Le Garite. And he doesn't care who he hurts in order to accomplish this goal.

As if the threat of imminent warfare wasn't enough, an eerie legend about the Voxes hovers over the Jersey Club's head: when the green, blue, and orange demons awake, the end of the world is nigh.

Viz Media originally held the license for the show's English release. When they lost the license, RetroCrush picked it up for streaming. Both the sub and English dub are available for viewing.

A manga adaptation titled Rinne no Lagrange: Flower Declaration of Your Heart ran from 2011 to 2013. A prequel manga called Lagrange: The Flower of Rin-ne ~Dawn of Memoria~ was serilized in Young Gangan from September 2011 to February 2013. Memoria focuses on the student lives of the couple of Kiss members that appeared in the anime.

A PlayStation 3 game called Lagrange: The Flower of Rin-ne -Kamogawa Dream Match- was released on August 23, 2012.

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This series provides examples of:

• 10-Minute Retirement: The three heroines decide to never fight with the Vox again in the middle of Season 2. This lasts for roughly one Breather Episode.
• 12-Episode Anime: Both seasons of the anime are twelve episodes long.
• Accidental Public Confession: Due to Madoka's monologuing in the space capsule while she in the body of Yurikano, the main characters learn everything about Yurikano's true feelings about her brother and fiancée fighting each other- she hates it.
• A Friend in Need: Madoka says she will always help a friend in need; even if it's a friend she just met, she'll pilot a robot for her.
• After the End: All the aliens are actually descendants of humans who left before Earth's civilization collapsed 20,000 years ago. Now their home planet is essentially a galactic reserve for society.
• Air-Vent Passageway: Madoka and Asteria use an air vent to get to Lan and Muginami, who're blocking the path to the Vox Aura to protest Asteria's decision to decommission it.
• Alien Among Us: Lan and Muginami mostly understand Earth culture, and Villagiulio is subject to Villains Blend in Better. Neither applies to Kirius, Izo, or Array, though they seem to have adapted by Season 2.
• Alien Arts Are Appreciated: Lord Vilagulio enjoys playing a hula hoop game on what suspiciously looks like a Nintendo Wii.
• Aliens in Cardiff: Kamogawa is a small, beachfront city that becomes a second home to a group of aliens. Said aliens use Kamogawa as their battlegrounds while using their mechs.
• Anti-Villain: Between their many humanizing scenes, lack of inclination to perform any actually villainous acts, and the show's Gray-and-Grey Morality, it's hard to see the Kiss Terrible Trio as anything other than people who's goal has placed them on the opposing side. Their boss, Villaguilio counts as well, since he wants to save his planet from a collision with another one, and feels he must destroy that one to do so. Dizelmine, the ruler of the other planet, qualifies as well for the same reasons. The only antagonist that doesn't qualify is Balance T. Moid, since he only cares about satisfying his curiosity.
• Apocalypse How:
  • The reason De Metrio and Le Garite are fighting is because their planets are going to crash into each other.
  • The Vox Units are also believed to be capable of destroying planets.
  • In the end, the events of the series alter the orbits of De Metrio and La Garite, solving the problem.
• Awesome Moment of Crowning: In the last episode, Lan is crowned as the ruler of Le Garite. Then she puts on her jersey.
• Batman Gambit: Lan and Muginami pull this off in Episode 17: Lan has Muginami thrown into the ship's prison, then distracts the guards with an overly long speech so Muginami can secretly escape and rescue Madoka with minimal interference.
• Barehanded Blade Block: Vox Aura handily catches Kirius' blade... and fails. Doesn't matter, because Vox Aura has thick plating (Kirius claims it was supposed to be nonlethal). In fact, this happens twice. The third time, it works, because Lan's robot does it that time.
• Batter Up!: Madoka bats away a flying newspaper dispenser, using a ripped-from-the-ground streetlight.
• Battle in the Center of the Mind: In Episode 17, Madoka and Yurikano have a mental slap fight.
• BFG: Villagiulio's Ovid has a mecha-sized gun. Latter on in the series, Lan receives a rifle as well.
• Big Bad:
  • In Season 1, Lord Villagulio, adoptive brother of Muginami and leader of the enemy organization Kiss, rules the planet De Metrio and rebels against the Jersey Club heroines, the Novumundos agency, and the Polyhedron Federation. In Season 1, his goal is to steal all the Vox Units and destroy the Polyhedron planet of Le Garite, but only because he believes the Vox Units can destroy the world, and the two planets are on a crash course with each other- he would really rather not destroy any planets.
  • In Season 2, Villagulio fights against and eventually gets overshadowed by King Dizelmine Fin E Ld Si, Lan's brother and the Polyhedron's leader who wants to destroy De Metrio. Both of them are in turn pawns of Balance T. Moid, a Mad Scientist Treahcerous Advisor who wants to open the Rin-ne and admire its beauty, even if it means causing the apocalypse in the process.
• Big Damn Heroes:
  • In Episode 11, Izo, Array and Kirius use their shields to protect Kamogawa from a Wave-Motion Gun.
  • Lan's brother and his Le Garite Knights in Episode 12 drive off Kiss just in time.
• Bitch in Sheep's Clothing:
  • Muginami seemed to be leaning towards this at the end of Episode 5, being a friend of Madoka and Lan but actually being The Mole and taking about war like it was nothing, but after Villagiulio's chastisement, she snapped out of it.
  • Dizelmine seems nicer than Villagiulio, but of the two, he's the one with the genocidal plans lined up as the first option.
  • Moid is the biggest example by far- his politeness and care-taking of Lan was a facade hiding a depraved Mad Scientist.
• Bittersweet Ending: Everything's resolved nicely by the end of the first season, but Madoka's two closest friends have left Kamogawa, without any indication as to when (or even if) they'll come back.
• Book Ends: The first season begins and ends with Madoka stripping to a swimsuit she was wearing under her clothes to help someone at the beach.
• Break the Cutie: Done to Muginami in Episode 5, after Villagiulio tells her that she is just a parasite and that she never was a part of his team.
• Bridge Bunnies: There are a few Nuvomundos employees who aren't given much screentime outside of their monitering of the Vox Units when they're in use.
• Butt-Monkey: Array constantly gets into various embarrassing situations, such as having to work for Asteria in a French Maid Outfit. And he seems to like it, seeing that he never took it off.
• Catchphrase:
  • Madoka often says "maru" (丸), which can mean both "circle" and "perfect".
  • Lan has "wan" (わん), the Japanese onomatopoeia for "woof". This is mostly due to being told that "woof" was another way of saying "hello" on Earth, but even after learning about that, she sticks with it.
  • Muginami has "Kashikomari!" (畏まりまし) (short for "kashikomarimashita") which can mean "certainly" and is translated here as "Roger that!".
• The Cavalry: The Le Garite fleet arrives just in time as Vox Aura stops moving. It's still possible to win the battle with the other two Voxes, but considering what happens when Vox pilots are pushed to their emotional limit, it's probably not a wise thing for them to do.
• Cell Phones Are Useless: Madoka's cellphone gets almost no reception in the floating city, but it somehow works just fine inside her robot and under hundreds of feet of ocean. The latter oddity is lampshaded by the commander.
• Chekhov's Army: The Le Garite fleet in Season 1 arrives to fend off Villagulio at the end.
• Chekhov's Gun: The shield materialization ability of the Ovids saves most of Kamogawa from the falling debris of the big battle (with the exception of Yoko, but she gets better).
• Cliffhanger: Episode 11 ends with Madoka's cousin being mortally wounded by a fallen enemy bot. Madoka sees this and has a Freak Out that causes all three Voxes to lose control and blossom simultaneously.
• Colour-Coded Characters: Each Jersey Club member is assosicated with a specific color: Madoka has green, Lan has blue, and Muginami has orange.
• Conveniently Empty Building:
  • The only building Madoka lands on in Episode 3 apparently shut down the previous week. She also manages to crash-land in an empty lot; the house that was there had recently been demolished. Although she didn't need to be that worried as an evacuation order was issued and the people were presumably heading to shelters.
  • Then there's Madoka's grandpa's peanut farm, which gets destroyed by her falling Vox Unit. This one is Played for Laughs.
• Crapsack World: Muginami's homeplant of U-Go is a barren wasteland, possessing little in the way of agriculture, pleasent wheather, and just general cheer. Her relationship with Villagulio is part of what helped Muginumi survive such a depressing enviroment.
• Creative Closing Credits: Both seasons include endings where the Jersey Club walks forwards and backwards on a series of chairs. The second season in particular has three different versions of this particular ending, one each for Madoka, Lan, and Muginami.
• Cross Counter: Madoka and Yurikano share blows while inside the Rin-ne, their punches connecting with their target at the same time as each other.
• Deflector Shields: Both the Le Garite and De Metrio flagships utilize large, circular shields to absorb any shots fired their way.
• Destructive Saviour: Madoka consciously does her best to avoid any destruction to her hometown of Kamogawa. It doesn't always work, especially considering that her Vox has a kind of special ability that plays right into Villagiulio's hands. Asteria actually forbids Madoka from using her Vox Unit for this reason.
• Distant Finale: Halfway through the final episode of the series, the plot skips some time to show what the main cast is up to some time after Madoka's graduation.
• The Dragon:
  • Grania is usually seen with Villagulio and taking orders from him. In his absense, she takes over the mantle of authority to direct her troops.
  • In Season 2, Moid seems to become Dizelmine's right hand, carrying out his orders and always being by his side, but he is actually The Man in Front of the Man.
• Dramatic Irony:
  • In Episode 9, Kirius runs into Madoka outside their mecha and neither of them recognize each other. Kirius even says later that he should have asked the girl he met where Madoka was not realizing that she was right in front of him.
  • In Episode 18: Madoka-in-Yurikano's body realizes that Yurikano is love with Dizelmine. She muses about this aloud in her escape pode before saying "If someday I meet Lan's brother again, I want to tell him how you [Yurikano] feel." She isn't aware that Dizelmine has been listening to all those musings.
  • Later on in that same episode, Dizelmine basically ends up confessing to Yurikano, thinking that she was still Madoka in her body, while the viewer knows perfectly well that they switched back.
• Earn Your Happy Ending: For all their struggles and heartbreaks, the entire series ends on a happy, positive and hopeful note. Madoka, Lan and Muginami are reunited for good, closer than ever, and has expanded the Jersey Club to include members across other planets, some of whom include Izo, Kirius, Array, Villagiulio, Grania, and Dizelmine; De Metrio and La Garite finally bury the hatchet; Yurikano is back from the Rin-ne for good and has reunited with her loyal understudies Izo, Kirius and Array; Lan ascends the throne of Le Garite in lieu of Dizelmine, who now travels with the recently-abdicated Villagiulio; and Asteria, finally free of her burden, travels together with Yoko around the world searching for more traces of the Rin-ne. The only person who doesn't get a happy ending is Moid, and considering that he was responsible for much of the misery in the series, it's a fitting fate for him to be apparently be stuck in the Rin-ne, forever doomed to listen to Madoka's heartfelt marching song (which he deemed dreadful) over and over.
• Earth-Shattering Kaboom: In the backstory, Yurikano blew up half a planet. Note that she didn't use the Vox to do it, but opened the Rin-ne with her own power.
• Easily Forgiven: Muginami is rather quickly forgiven for being a spy who was planning to give the Voxes to Villagiulio. Madoka apologized to her. To her credit, Muginami does make an effort to be a true friend and ally.
• Elemental Powers: Vox Aura, Lympha, and Ignis are stated to have the powers of wind, water, and fire, respectively. More Informed Ability, as this is never demonstrated.
• Embarrassing Tattoo:
  • All three of the main girls have a Memoria symbol in unusual places. Madoka's is possitioned on the lowest part of her back, Lan's is somewhere near her breasts, and Muginami's is just above her crotch.
  • On the other hand, Asteria's tattoo, that which she calls Rin-ne, is located right on her bosom.
• Empathic Weapon:
  • The Vox units only work if the pilot believes in themselves. Madoka seems to have "befriended" hers at some point in the past as well.
  • Near the end of Season 1, Vox Aura begins glowing even when Madoka's not anywhere near it, and in Season 2, all of them move on their own to rescue their pilots.
  • In Episode 23, Aura actually sends Madoka an e-mail.
• Everyone Lives: Although Moid gets banished to the Rin-ne, so he's effectively dead. Other than that, no character dies permanently.
• Evolving Credits: Episode 12 replaces the OP with the ED, and Episodes 16-18 and 22-23 have a completely different ED than the one for the earlier episodes of Season 2.
• Fanservice: Quite a bit. The suits are rather skintight and show off the back, and the girls get jobs working at Be With Hiroshi wearing waitress outfits.
  • In the first episode, Yoko drops Madoka's pants, resulting in Comedic Underwear Exposure, and there's also a Shower Scene with Madoka, where Lan sneaks in undetected and unintentionally scares her.
  • Season 1 Episode 7 has a Bathtub Bonding scene, spontaneous Skinny Dipping, and a bunch of eels wriggling around and attacking girls in a manner clearly evoking Naughty Tentacles.
  • Season 2 Episode 8 has Reiko trip and accidentally yank Muginami's towel off during art class, exposing her body which she quickly covers up.
• Fanservice with a Smile: When Lan and Muginami help Madoka out at the restaurant, nearly the entire town gathers there due being told about "a cute waitress and a klutzy one?". And almost everyone sits there gawking at Lan spilling everything and at Muginami's Buxom Beauty Standard figure. Later, they all get waitress uniforms.
• Fashionable Asymmetry: When wearing her jersey, Madoka has the right pants leg and left jacket sleeve rolled up.
• Forceful Kiss: When it seems like neither Lan nor Muginami can let go of their hostilities towards each other due to the war between their respective nations and each girl's opinion on involving Madoka into it, Madoka forces the two to kiss each other and gives a Rousing Speech to make them both re-join the Jersey Club. Afterwards, Muginami makes Madoka and Lan kiss each other for fun, then Lan tries it on the other two when they start heckling her. Lan only succeeds in making them headbutt each other.
• "Freaky Friday" Flip: In Season 2 Madoka switches bodies with Yurikano. It abruptly ends when Madoka-as-Yurikano touches Dizelmine.
• Furo Scene: Madoka, Muginami, and Lan take a bath in the Le Garite's mainship before dressing up for a formal dinner with Lan's brother, Dizelmine.
• Gilligan Cut: In Episode 14, Madoka attempts to leave the island base Pharos. Tadokoro lets her go because there are no ships to take her to the mainland, and he thinks that she cannot possibly leave. Cue to the next scene, where Madoka finishes swimming to shore.
• Go-Karting with Bowser: Then they have a drink to make up for their immaturity. Villagiulio gets the coat.
• Grey-and-Grey Morality:
  • Everyone's motives are very vague at best- the only thing we can be sure of is that Madoka wants to protect Kamogawa, and everybody else isn't making it clear why they're fighting. The villains are actively trying to avoid causing collateral damage to the Earth and in general aren't that bad of people, they simply want their weapons back when it's not really told why they're on Earth in the first place.
  • Things get slightly less grey in the space war in Season 2, where Prince Dizelmine intends to destroy De Metrio to save Le Garite while Villagiulio outright says he will not be like Dizelmine.
  • By the end everyone becomes a lighter shade of grey, except for the true Big Bad.
• Human Alien: All of the aliens that have appeared thus far. Justified because they actually are descendants of Earthlings that voyaged to other planets before Earth's civilization collapsed.
• Humongous Mecha: The Voxes and the Ovids. The Vox double as Transforming Mecha and Emphathetic Weapon.
• Hyperspace Is a Scary Place: Moid says that the Rin-ne connects people's minds (or something to that effect), but it rarely has a good effect when it intrudes into the real world. He turns out to be lying though.
• Idiosyncratic Episode Naming: The series puts the name "Kamogawa" in every episode title including the OVAs. Kamogawa is the city where the show is set.
• Improvised Weapon: For the first couple of fights, the Vox units don't get any weaponry whatsoever, forcing Madoka and Lan to punch and throw random crap to victory. Later on they get actual weapons sent to them.
• Indirect Kiss: Yoko's apprentice was ecstatic in Episode 6 at the prospect of sharing one with her when she took his instant noodles from him.... only to finish it and throw the cup in the bin, visibly disappointing him.
• It Meant Something to Me: Muginami's reply to Lan's questioning her intentions was that it was a good time, but the good time must go. Then they make up later and Muginami becomes a permanent member.
• Laser Blade: Izo, Kirius, and Array's robots each have one. Voxes Aura and Ignis later gain them as well.
• Locked in a Room: In Episode 16, Asteria conspired to get Villagiulio and Dizelmine locked in an elevator to get them to make up and stop the war. Ultimately proves fruitless, as they continue fighting anyway.
• Loophole Abuse: Madoka's teacher announces there is no regulation that says students can pilot robots. Commander Tadokoro counters by indicating there's nothing that says students can't pilot robots either.
• Male Gaze:
  • Female-on-female, but Madoka's first view of Lan is the full slide up with her slack-jawed.
  • Quite a few shots have a female character's rear end covering half the screen.
• Mecha Expansion Pack: The Vox units get one about Episode 10. It gifts Muginami with a double-bladed sword, Lan with a machine gun, and Madoka with a smaller Laser Blade.
• Mental World: Rin-ne is more or less the collective unconscious.
• Mood Whiplash:
  • Lan and Madoka successfully beat the bad guys with The Power of Friendship. Then Array recounts a legend that essentially amounts to "the Vox units will destroy the world".
  • In Season 2, after Madoka in Yurikano's body is sent into Le Garite in a space capsule:
  "Goodbye, Lan. Goodbye, Muginami. Goodbye, Earth."
  (Beat) (Vox Aura launching itself to pick up Madoka's capsule and fly back to the general direction of Earth)
  "Everybody! I'M BACK!"
• Must Make Amends: Lan feels very bad for making Madoka pilot the Vox Aura and for the destruction that Kamogawa suffers from battle. But Madoka doesn't think badly of her, since being a pilot is Madoka's own decision.
• New Transfer Student: Both Muginami and Lan transfer into Madoka's school in Episode 4.
• NGO Super Power: Novumundos is ridiculously powerful. Asteria casually threatens to replace the American president during a phone call.
• No Romantic Resolution: The trio is together at the end, but seemingly still only as close friends.
• Obviously Evil: Dizelmine in Season 2 is very secretive and often downright villainous to everyone he supposedly cares about, is Ax-Crazy half the time, and has genocide as option one for the season's conflict.
• Oh, Crap!: Possibly the prettiest one ever; making an explosion that resulted in green energy flowers falling everywhere looks harmless, but the resulting Evil Laugh from Moid and Villagiulio's relative approval of the event sure as hell don't mean good things.
• On the Next: Each episode contains a preview for the next episode, the voiceovers of which are hilarious conversations between the cast, often completely unrelated to the footage actually being shown.
• One Dialogue, Two Conversations: In Episode 9, Izo re-enacts a samurai drama on TV in an attempt to indicate that he wants to fight Madoka... and the people listening thinks he wants to confess his love to her, or that he is her boyfriend.
• Only the Chosen May Wield: The Vox Units. This trope is called "Memoria" in-universe. Notably, Madoka seems to have been chosen by Aura when she nearly drowned, while Muginami was chosen when she touched Ignis while naked.
• Paper-Thin Disguise: In Episode 16, Madoka and Muginami do this to sneak onto the Le Graite ship. Madoka’s disguise consists of overalls, a pair of glasses, a different hairstyle, and (in the English dub) an obviously fake southern accent, while Muginami simply wears a dress and headgear. Dizelmine and Moid see right through them, but let them on anyway.
• Phlebotinum Killed the Dinosaurs: The Voxes triggered the Last Glacial Maximum, destroyed the human civilization of that era, and forced the survivors to flee to outer space, their descendants today being aliens like Lan. No wonder Kiss is hellbent on destroying the Voxes.
• Polyamory: This is one interpretation of the relationship between Madoka, Lan and Muginami by the end of the series, fueled by the huge amount of subtext between them all.
• Posthumous Character: Yurikano, Lord Villagulio’s bilogical sister who happens to look like Madoka. Subverted, as she's Not Quite Dead thanks to her fiancée King Dizelmine keeping her alive, and plotting to switch her body with Madoka.
• The Power of Friendship: The Vox seems to work better when using this. This and The Power of Love are what Madoka intend to use to stop the war between De Metrio and Le Garite; they've been used to successfully re-friend Lan and Muginami.
• Precursors: Earth itself is actually the origin of the Polyhedron alien cultures, in fact being the descendants of human colonies from a lost age gone twenty thousand years ago.
• Prequel: The Dawn of Memoria manga deals with Izo, Kirius, Array and Yurikano while they were still in the De Metrio military academy.
• Pretty Boy: The three attackers of the earth, Izo, Array, and Kirius, are incredibly handsome alien men whose good looks attract a lot of attention from the Kamogawa girls and women.
• Product Placement:
  • Drink sweet energy drinks◊ and you'll be able to save the earth!
  • The credits mention it's sponsored by Nissan to a degree, as well as the mechs being created by Nissan's vehicle designer.
• Pseudo-Crisis: Episode 12 actually begins two weeks after the Cliffhanger in Episode 11, showing everything is fine. We only learn what happened later in the episode.
• Pseudo-Romantic Friendship: Madoka is very, very close to both Muginami and Lan. (Despite Lan's misgivings, she has no problem with having two people be her Most Important People.) Madoka and Lan star in the blatantly romantic student film "The Spaceship and the Lily", and the false declaration of love turns out to not have been so false. In Season 2 Episode 2, they start declaring their love for each other.
• Quirky Miniboss Squad: Kirius, Izo, and Array. They pull a Heel–Face Turn.
• Real-Place Background: Kamogawa is an actual seaside city in Japan. It's located in the Chiba Prefecture, and most if not all of the places shown in the anime, like the Sea World, are places you can actually visit.
• Reality Warper: Essentially the ultimate power of the Voxes through entering Rin-ne.
• "The Reason You Suck" Speech:
  • Muginami calls Madoka out in Episde 6, claiming that she doesn't truly think of others and that everything she does is for selfish reasons. It does nothing but piss Madoka off, and makes her enable the Rin-ne.
  • In Episode 7, Madoka realizes that Muginami was right and that she needs to learn to listen to people.
• Recap Episode: The "Kamogawa Memoria" OVA recaps the events of the first season, all narrated by Madoka's cousin, Yoko.
• Red Herring: Season 1 drops some implications that Lan's brother is dead but it turns out he's been alive and well. A similar thing occurs with Yurikano, who's Not Quite Dead.
• Red Oni, Blue Oni:
  • Muginami and Lan.
  • Also their brothers, Villagiulio and Dizelmine.
• Relax-o-Vision: Happens in Episode 15 when Asteria says very naughty things to Madoka, simply to get a reaction.
• Rule of Symbolism:
  • The three colored chairs that represent Madoka, Lan, and Muginami. At the end of episodes that mark important turning points in their characters, the chairs shift positions and placement. [[spoiler:In Episode 11, they go flying into the air, imitating the three Vox Units going crazy. At the end of the first season, Madoka's chair is all alone, as is Madoka herself since the other two left to return to their respective home planets.
  • Season 2 continues the colored chair symbolism, but this time they show up in odd places, such as Madoka's chair appearing in the place where Yurikano performed her Heroic Sacrifice. In Episode 23, Yurikano appears with the chairs. In Episode 24, the last image of the series is of the three girls sitting in their respective chair.
• Rule of Three: Yoko discusses this trope with Asteria the importance of Madoka in any relationship, the most important ones being Lan/Muginami and Villagiulio/Dizelmine. Three is a common number that is explored in mythology and religion. One cannot do everything on its own, and two would easily break away and destroy themselves based on their vast differences. Only three, with the third being a moderator, is there stability.
• Running Gag:
  • Madoka's inability to pronounce Villagiulio's name.
  Madoka: "Villagiuvio!"
  Lan: "You almost got it right."
  • She still can't get the hang of it in Season 2, where she screws up Villagiulio's name in an unsecured broadcast to his ship, pissing off his second-in-command Grania and Commander Tadakoro, but makes him crack up and muse how she hasn't changed. She settles for Giuvi in the end.
• Scenery Gorn: Muginami's home planet of U-Go is broken, gray, stark and an overall horrid place.
• Scenery Porn: Vibrant and lush surroundings. Even the metaphysical apocalyptic scene after Rin-ne fully blooms is astonishingly nice-looking, if depressing.
• Seiza Squirm: Asteria makes Izo, Kirius and Array do this in her office after they lose track of Madoka.
• Shipper on Deck: The girls who produce the student film "The Spaceship and the Lily" (starring Madoka and Lan) are implied to be a bunch of Madoka/Lan shippers.
• Shout-Out:
  • In Episode 8, the Voxes buzz the command bridge and make Tadokoro spill coffee on his shirt, just like this scene from Top Gun.
  • One of Madoka's Jersey Club odd jobs in Episode 12 is serving as a poetry reader in a game of karuta. Probably not a coincidence that this series aired in the same season as Chihayafuru.^note Lan and Muginami's seiyuus are the same as Chihaya and Kanade.
• Skinship Grope: No groping, but naked bathing and hugging.
• Space Elves: The Polyhedron people. Lan especially fits the naive elven princess archetype.
• Starship Luxurious: Le Garite's flagship, which has enough room for an entire mall and a full-scale replica of Kamogawa.
• Strategy, Schmategy: Madoka has no idea what the hell she's doing at first. Her random flailing moves confuse Kirius, who begins thinking that they're immensely powerful Earthling combat techniques that he's never fought before.
• Take a Third Option:
  • Instead of having to choose either Lan or Muginami's side of the war, Madoka uses The Power of Love and Friendship to make the two stop fighting each other. Afterwards, Asteria recommends that Lan and Muginami seek asylum on Earth.
  • Vox Particles appear during times when the pilot is in a high emotional state, with anger, sadness or hatred being the easiest to stir up. When Novumundos wants to try out the Vox Particle Control Experiment, it seems like they might have to either risk putting Madoka through the same trauma as Lan did during Moid's experiment. Turns out Madoka is either so resilient or so dense that she doesn't respond to the expriment's stimuli. Asteria notes that shame works as well as the other emotions and proceeds to tease Madoka about her being a virgin and let's her imagination do the rest.
• Telepathy: The Voxes facilitate the transfer of thoughts. At the end of Season 1, Madoka actually hears the thoughts of everyone in Kamogawa.
• Thanks for the Mammary: Completely out of the blue, Asteria sneaks up on Madoka and grabs her breasts. Madoka actually seems pretty disturbed by the sudden groping, but the event is quickly forgotten.
• Tokyo Is the Center of the Universe: Kamogawa is about the only part of Earth that's involved in the story. Lampshaded at the beginning of Season 2, where a couple of Madoka's classmates remark that Kamogawa has suddenly become more important than Tokyo.
• Transforming Mecha: The Voxes have two forms: a default airplane mode and a bipedal fighting mode.
• Trouser Space: Madoka pulls a tennis ball out of her skirt. This is actually◊ Truth in Television.
• Trippy Finale Syndrome: Happens in the end of Season 1, bordering on Gainax Ending if it weren't for the fact that not all of it is a Mind Screw, and the parts that are get a Mind Screwdriver in Season 2.
• True Companions: According to Madoka's older cousin, True Companions are people carrying the same beliefs and holding mutual love for each other. Madoka, Lan, and Muginami grow into this as the series goes on.
• Unspoken Plan Guarantee: Lan and Muginami's plan to rescue Madoka from Dizelmine doesn't become apparent until Lan is into her broadcasted speech. When Muginami yanks the cell key from Victoria's Secret Compartment, it becomes clear that Lan's earlier supposed Face–Heel Turn was merely a distraction.
• Unusually Uninteresting Sight:
  • The kids at Madoka's school don't seem to notice Lan's blue hair, purple eyes, and her unusual outfit. They just wonder if Madoka finally recruited a new club member. Even Madoka herself doesn't take notice of it.
  • In a mixture of Cloudcuckoolander and Crazy-Prepared, Madoka thinks Lan's costume is a swimsuit, and that she's prepared for a rescue, just like herself in the beginning of the episode.
• Villain Decay: Kirius, Izo, and Array. Though they make pretty poor villains to start with, they eventually become mere waiters at Be With Hiroshi, and do a Heel–Face Turn.
• Villain Episode: Episode 9 is centered around Kirius, Izo, and Array, where they show their comical misunderstandings of Earth society.
• Villains Out Shopping:
  • Villagiulio is shown playing a dancing video game at one point, and at another gets in a fight with Madoka's uncle Hiroshi over a coat they both wanted to buy.
  • Episode 9 is almost completely this, in which Kirius, Izo, and Array go about their business, get into hilarious misunderstandings, and bicker with each other.
• Walking the Earth: At the end of the series, Yoko and Asteria actually are walking the Earth, while Madoka, Lan and Muginami are continuing their Jersey Club activities throughout space.
• War Is Hell: It's all but stated that Lan lost her brother in a war sometimes in the past. It's a Red Herring; Dizelmine is very much alive and the Disc Two Final Boss. This is also the reason why Villagiulio doesn't regard Muginami taking a Vox as a good thing, since to him, she's just a war-buddy-wannabe kid.
• Was It All a Lie?: When Lan corners Muginami about secretly working for Kiss, she asks her if Muginami's friendship was all a facade.
• Wham Episode: Episode 11 includes Madoka underging a Heroic BSoD and nearly opening the Rin-ne, her friends being forced to do so as well, and the apparent incoming appolopsye, all while Dizelmine, Moid, and the Polyhedron Federation are looking less benevolent than they initially seemed. The world is saved by the next episode, but the plot threads are further explored from there.
• Wham Line: In Episode 20, Dizelmine is secretly meeting Moid, the later of whom shows Dizelmine his torso covered in some familiar looking symbols.
  Moid: Yes. It is the Memoria I was imprinted with 20,000 years ago.

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"Perfect!"