Characters

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I know it's a bit hard to tell what's going on in the comics sometimes; the body language of polyhedrons can be a bit difficult to parse. To make that at least a little easier, all characters on this page are facing to the right. (Except The Buddha, to whom facing doesn't actually matter so very much.) Other than that, you're on your own; I had just as hard a time figuring this stuff out as you did.
Dido is a whimsical shape, largely devoted to keeping a little bit of chaos in everyone's lives. It doesn't actually have a gender; a rarity among the Polytopes. Would almost definitely be a Discordian, had it ever heard of it.

Special Ability: Portal creation. Ever since it blew a hole in the unverse, Dido has had tenuous control over a swirling blue vortex called "the Rift". The Rift's destination is completely random unless Dido can see the destination in advance.
Pinky has the same issue as Dido, but in the opposite way: her gender is set, but no one can agree on what it is. As such, referring to him can get a little confusing. She doesn't mind, though: Pinky is contemplative and accepting of most things. He doesn't talk much, but her words hold much sway in the Negatopes household.

Special Ability: Unknown.
The puppy was brought into the house under as-yet-unexplained circumstances. She seems utterly devoted to Dido and its mischief. Her bark is an odd utterance, seeming to come from everywhere and nowhere at the same time.

Special Ability: More like adorability!
The Ol' Hound Dawg is a crotchety old curmudgeon, through and through. He sips thin gruel and drinks bland tea and generally spends most of his time yelling at people or reminiscing about his army days. Which army is unclear, since no one can remember ever being outside the torus, but still.

Special Ability: Unknown.
Seen here, as almost everywhere, in a sort of three-quarters view, Otto is the most logically-minded of the Polytopes. (It's all those rigid angles.) Hates the Buddha for his incessant puns. May or may not have a drug problem (he recently cooked up a batch of LSD for reasons as yet unknown).

Special Ability: Otto is good at science and other knowledge-based pursuits, but only to an extent. His attempts usually end in confusion. Also he can repair "that which has been broken".
Rondo is like a second Buddha in the Negatopes universe, or at the very least an Ananda. He likes wordplay and being groovy, and while he's not as universally perfect at it as The Buddha, he does try harder.

Special Ability: Paronomasia.
Ike is the naive artist of the hypercube. She seems pretty flighty most of the time, and that's because she is pretty flighty, but she's got a good heart and a kind disposition. Has recently begun writing on a typewriter from another dimension. Infatuated with Brock.

Special Ability: Opening windows to alternate realities. They don't go anywhere, unless Dido uses its ability in tandem.
Spike is brimming with the technical and scientific intelligences, much in the way that Ike can barely contain her creativity. He likes to think about parallel universes, draw schematics of how they might line up, et cetera. If he did have access to the typewriter, he'd probably use it to write bad speculative genre science fiction.

Special Ability: Awareness of/in at least four dimensions.
Brock is a bit on the slow side. He likes playing games, though, whether he wins or not, and he's got a kind of charm if you're willing to give him the benefit of the doubt.

Special Ability: Indomitable levity.
Feldspar is right up there with Spike on intelligence, but in more of a "general knowledge" kind of way. This is mainly because he is a direct foil for Brock's general obliviousness. He also foils Brock's emotional state; Feldspar is almost always bitter about the injustices of the universe.

Special Ability: Unknown.
The Buddha is The Buddha. Everyplace has to have one, right? Now that we know about the Negatopes universe, it's becoming increasingly clear that everyplace has the same one. He has no angles or sides and is partially transparent, both of which are signs of his enlightened state of mind. Loves hanging out and wordplay. Motives as yet unknown, probably related to compassion for all sentient beings.

Special Ability: Enlightenment.
Tess is a tesseract, the four-dimensional equivalent of a cube. She's a bit of a ditz, but that's understandable when you live entirely alone in an empty universe. She is the house in which all the other Polytopes live, and may have a vague awareness of the goings-on on her three-dimensional "surface".

Special Ability: Unknown.
The Pair O' Ducks is just that. For a while I had plans to call them Duck X and Duck Y, but it turned out a lot of users had trouble reading the "Duck X" format. Pair O' Ducks it is.

Special Ability: Speech, but only sometimes and usually about paradoxes.