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Euclideans are an interdimensional species. They are depicted as two‑dimensional, reality‑warping entities native to the plane known as Euclydia, a flat universe destroyed in an event later termed the Euclidian Massacre. Bill Cipher is the only known surviving member of the species and serves as the primary source of information about their biology, culture, and metaphysical properties.
Overview
Euclideans are portrayed as two‑dimensional geometric beings with mutable forms, advanced perceptual abilities, and a natural affinity for interdimensional manipulation. Although little is shown of their society, canonical and semi‑canonical sources describe them as a civilization of “flat minds in a flat world,” governed by strict prohibitions against discussing higher dimensions. Their destruction is attributed to Bill Cipher, who annihilated the species and their universe in a catastrophic act of reality‑warping.
Biology and Physiology
Note: It's unknown if the powers and abilities demonstrated by Bill Cipher are inherent to the entire race or if they're unique to Bill. Their blood is made of static, which is why Bill is scared of TV static.
Dimensional Nature
- Euclideans exist natively in two spatial dimensions, perceiving only length and width.
- Bill Cipher’s mutation—an enlarged eye capable of perceiving the third dimension—is described as a rare and socially stigmatized anomaly.
Physical Form
- Members of the species appear as geometric shapes, most commonly triangular.
- Their bodies exhibit:
- A single central eye
- Floating limbs not fixed to anatomical positions
- Brick‑patterned lower bodies
- Variable size, from hand‑sized to building‑sized
- Euclideans lack mouths but can simulate speech and consumption through their eye.
Perception and Cognition
- Euclideans possess:
- Pan‑dimensional awareness (in rare cases)
- High cognitive plasticity
- Innate reality‑editing abilities within their native plane
- Their society enforced strict bans on discussing or perceiving the third dimension, suggesting cultural fear of higher‑dimensional cognition.
Known Euclidians
- Bill Cipher
- Scalene
- Euclid
- A random rhombus-shaped Euclidian
- A random trapezoid-shaped Euclidian
Abilities
Innate Abilities
Euclideans demonstrate:
- Reality manipulation within their home dimension
- Dream infiltration and mindscape traversal
- Illusion creation
- Telepathy and clairvoyance
- Contract‑binding metaphysics, enabling deals with mortals
These abilities appear amplified in non‑physical or dreamlike spaces.
Limitations
- Euclideans require summoning rituals or dimensional gateways to access higher dimensions.
- They cannot enter a conscious mind without consent, typically via a handshake‑based contract.
- Their powers are constrained by dimensional laws outside their native realm.
Culture and Society
Social Structure
Little is known about Euclidian society, but available information suggests:
- A highly conformist culture
- Legal prohibitions against discussing the third dimension
- Celebration of birthdays as civic events (Bill's birthday was declared a national holiday)
Technology and Knowledge
- Euclideans possessed advanced metaphysical knowledge but appear culturally stagnant.
- Their understanding of higher dimensions was suppressed, possibly due to fear of destabilizing their reality.
History
The Euclidian Massacre
The destruction of Euclydia is described as the central catastrophic event in Euclidian history. According to Bill Cipher's fragmented recollections, the incident occurred when he attempted to expose his species to higher‑dimensional knowledge, an act he framed as a form of liberation. During this process, he reportedly lost control of the dimensional forces he invoked, triggering a plane‑wide conflagration that resulted in the annihilation of the Euclidian population, including his own family, Scalene and Euclid. Bill's account of the event is considered unreliable due to significant memory impairment associated with trauma, dissociation, and psychological defense mechanisms. In the show, Bill says he killed everyone on purpose, but in The Book of Bill, he says it was an accident.
Survival and Extinction
Bill Cipher is the sole confirmed survivor of the Euclidian Massacre, the event that resulted in the destruction of his species and their native plane. His subsequent emergence as a powerful entity within the Nightmare Realm, along with his later interactions with the third dimension, constitute the primary sources of the Euclideans' narrative relevance. Semi‑canonical materials, including The Book of Bill and the Axolotl poem, suggest that Bill may reincarnate "in a different form, a different time," and imply that Euclideans could persist as metaphysical echoes or karmic remnants. No additional members of the species have been depicted in canonical or semi‑canonical works.
Quotes
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"Why did you do it?" |
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"The sky is on fire. Everything is burning. How could this happen? You killed us all. Remember us." |
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"The murderer's name is Bill. The sky's on fire. Everything is burning. You killed us. Remember us." |
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"Rockabye, Billy, please don't you cry. It's not your fault, you have that strange eye. Stay safe with mommy, you'll never fall. And we'll always love you, sharp angles and all." |
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"“Oh little Billy wore velcro until he was sixteen. He said shoelaces were fascist but we really think he just couldn’t figure out how to tie them”" |
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"TWO DIMENSIONS TO AND FRO, YOU ALWAYS KNOW WHICH WAY TO GO IF YOU'RE LOST, DON'T BE AFRAID! IN EUCLYDIA, YOU'VE GOT IT MADE RUN TOO FAR TOO RIGHT OFF FRAME? YOU'LL APPEAR ON LEFT AGAIN! JUMP TOO HIGH? DON'T CRY OR FRET! YOU'LL POP UP FROM THE GROUND, I BET! IN THIS SPACE, THERE IS NO FEAR, LOVED ONES WILL BE EVER NEAR, ROLES AND RULES ALWAYS CLEAR, EUCLYDIA WE HOLD YOU DEAR" |
Trivia
- With the death of Bill Cipher - who was supposedly the last of his kind - the Euclideans are now extinct.
- There is one atom of Euclydia left under Bill's hat.