#euclydian

reference:

Haha.. I uh.. I like @orxinus 's simple Bill... 🤤 ermm.. *wipes off spit* please ignore that me making human eradicates a lot of the mystery element to mm!ford, I just wanted to have fun

Rest in peace, Simple Bill, you would've loved Annie (1982)

why did you do it, billy?

Part 1, Part 2, Part 3, Part 4, UPDATE

I have never in my life imagined that I will continue this series, but I am doing it, thanks to some of my insane fans who asked for this. In this part I will talk about developmental biology of Euclydeans which is probably the biggest challenge so far.

As always, this analysis is based on two assumptions:

Before Bill Cipher became a demigod, he was a biological, living organism and so were the rest of his species.

Even after Bill Cipher became a demigod, he still retained some physical characteristics of his biological form.

And a fair content warning: This contains anatomy illustrations. This isn't anything gory, but there are people who are squeamish, so you've been warned.

Click on the images to get better quality!

And without further ado, let's begin.

Euclydean Body Plan

A body plan (also called Bauplan) is a morphological quality of an animal which can tell us clearly to which phylum it belongs. An arthropod will have a very distinct body plan from a vertebrate for example. Body plans are coded by Hox genes in animals and they determine the way an animal's body is going to develop from embryonic stages to adulthood. Euclydeans are aliens, so they don't have Hox genes, but they probably have something similar. Even if they don't have DNA (and they most likely don't), they still have some way of passing their traits to their offspring, which is essential for every living organism. Since I don't have any other option, I will call them genes and genomes.

The body plan of a Euclydean is relatively simple. They are bilaterally symmetrical, shelled, invertebrate organisms. The shell can take three distinct shapes: a triangle, a trapezoid and a rhombus (or a square, but remember, squares are rhombuses that have all four angles at 90 degrees). I haven't found mentions of any other polygons anywhere, but if you did, please tell me.

The shape of the shell was a status symbol within Euclydean society, with triangles being the lowest and squares the highest class. I was thinking about why that would be and after spending an insane amount of researching, I think I found a plausible (although most likely not true) answer: Polyploidy.

Polyploidy is a phenomenon in which the entire genome duplicates. It's very common and often encouraged in plants, since it makes fruits larger or fruiting period longer. Wheat, tomatoes, strawberries, corn and many more plants that we grow are polyploid. In most animals, poliploidy is lethal. It is lethal in humans. But some species or annelids, mollusks, insects, fish and amphibians can be polyploid. My favorite example of polyploidy is in green toads (Bufotes spp.) where polyploidy forms a species complex.

I won't go too far into toad genetics here, but in central Asia, there is a species of green toad that is diploid (like humans - it has one copy of its genome from the father and one from the mother) and one that is polyploid (4n - tetraploid - has two genome copies from each parent). When these two hybridize they create a third species which can be either, but it often has characteristics that place it "in between" the two other species. This hybrid species is fertile and can mate with the other two and that's how you get a species complex.

I believe that Euclydeans are a similar species complex. Triangles would be diploid in that case and rhombuses would be 4n tetraploid. (Because a rhombus basically is two triangles stuck to each other. Duplication of an entire genome could result in something like that easily.) Trapezoids would be a hybrid between the two.

So, triangles are 2n diploid, rhombuses are 4n polyploid and trapezoids are 3n hybrids. Each of these can mate with any other, but the offspring will be different, depending on the pairing. Two triangles will always have a triangle child. Two rhombuses will always have a rhombus child. A triangle and a rhombus will always have a hybrid trapezoid child. Two trapezoids, however, will have a trapezoid child in 50% of cases, whilst 25% will be triangles and 25% rhombuses. A trapezoid and a triangle have a 50-50% chance of having a child trapezoid or a triangle. A trapezoid and a rhombus will have 50-50% chance of their child being either a trapezoid or a rhombus. I made you a graphic, so you can understand easier:

What this essentially means, is that whenever someone mates with a triangle, their ploidy (the numbers of genome copies they have) will lessen, whilst mating with a rhombus will cause it to increase. Since Euclydean society valued more symmetrical and more polygonal rhombuses, this was probably the reason why triangles were the second class citizens. Trapezoids have only 25% chance of having a triangle child, so their marriage might be scrutinized and policed if that was the case (maybe that's what Bill's erotic novel was about?)

Embryonic Development

This was requested by one of my fans (all of them credited below) and it was honestly the biggest challenge ever put in front of me, but I don't give up easily!

One thing that we certainly know about Euclydeans is that they are bilaterally symmetrical. This means that they have a left and a right side. Since this is the case, their ancestors were probably like this as well. But, Euclydean shells also have radial symmetry (which means that you can draw symmetry lines from one tip of the angle to the other, or to the base of other side from every angle). Luckily for us, Earth has something like that too: Echinoderms (sea stars, sea urchins, sea cucumbers and some other groups).

Echinoderms are almost all radially symmetrical, but they have evolved from a bilaterally symmetrical ancestors. This is further proven by their larvae being bilaterally symmetrical too. I believe that Euclydean embryos probably look more like a bilaterally symmetrical organisms, similar to bipinnaria larvae of sea stars. But, as the embryo further develops, they become more "shaped" and gain the radial symmetry as well.

As we all know now, Euclydeans reproduce sexually. Their embryos develop inside a uterus of a parent (which could be both a male and a female, since many people pointed out to me that they are very likely hermaphrodites, which absolutely checks out). Since Bill claimed several times that both Ford and Mabel should have eaten their twins in the uterus, I proposed the idea of oophagy (or adelphophagy) as the means by which Euclydeans feed their offspring in utero. This is further proven by that silly image from thisisnotawebsitedotcom.com where Bill drew himself as a baby in uterus, but he had a bottle of milk in one hand. He obviously doesn't know much about humans and placental mammals, but since he was older than 16 when his dimension was destroyed, it's very likely that he had sex education in school, so he knows how Euclydean babies feed in uterus.

Oophagy simply means that the mother produces many yolk rich eggs that her baby will be able to consume as it grows. If some of those eggs are fertilized, besides the one that will become a baby, then we're talking about adelphophagy where one, strongest embryo hunts down other embryos as food. Sharks are probably most famous for this, but several species of wasps and marine snails also practice it. Bill might have had a slight advantage over his other siblings because his eye (and consequentially his mouth) were larger due to his unusual mutation.

Euclydeans are shelled, but their shell does not develop fully inside the mother. Similarly to some species of oysters, young that grows inside the mother begins to develop shells (in oysters, this stage is referred to as "veliger larva"), but they are expelled out before the shell fully hardens. This is in order to protect the mother's insides. Unlike oysters, Euclydeans have just one (or maybe very rarely two) children at a time, so their baby is large. Judging from the size of the vaginal slit, it's probably around a third of their parent's size. That's very big (average human baby is just about 6% of the mother's weight), but Euclydean babies are born fully developed, with the exception of the shell. The shell fully develops when they begin to molt and so it hardens, looking more triangular (or any other shape, I don't know how to say that in English).

Here's the anatomy of the embryo and fetus in various stages of development. I don't know the specifics of anatomy of any Euclydean besides Bill Cipher, so it's him depicted here. Who asked for baby Bill's organs? Nobody, but you have them now:

So, this was everything I have proof of. But, in my shitty fanfiction "Bad Triangles Go to Therapy", I proposed that Euclydeans could have periods. I did this as a joke, but they could. Probably.

Since adelphophagy is extremely taxing for the mother, she would have a baby only every few years. But, if she somehow skipped this fertile period, she would have to expel all of the eggs that her body formed. This could be, or feel like, a menstruation, but they wouldn't shed uterine lining, just the eggs. Alternatively, a mother could simply reabsorb the eggs. This way, she would keep all of her nutrients inside her body and recover faster for the next fertile period. This is completely up to interpretation, because I have no idea.

@aroacejedi was the one who asked for embryonic development of Euclydeans, whilst @equilateralbill was the person with whom I discussed the logistics of Euclydean reproduction in more detail. They are the ones you should thank for this bullshit.