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Old Superdimensional Glossary

The Superdimensional Glossary

This is a glossary of my preferences for my superdimensional (≥4D) vocabulary, with most of them being 4D terms. There aren't really too many stardards set in place, so you can kind of make up whatever you want for now...

There are also Latin translations for some novel terms, because why not. Hover for its declension (genitive case) and gender.

This was partly inspired by Hi.gher.space's Multi-dimensional glossary.

Key:
! : well-recognized term
verbum^&: Latin etymology, hover (for non-trivial terms, at least)
underline: made up word, hover for pronunciation and etymology

Geometry

Some terminology

! surcell supercella: the 3D surface of a 4D shape.

surter superteron: the 4D surface of a 5D shape.

! realm campus: the 3D cross-section of a 4D space.

! flune flūna^&: the 4D cross-section of a 5D space. Adjective flunar.

! cell cella: the 3D equivalent of a side/face.

! teron teron: the 4D equivalent of a side/face.

(dia)triaxonal diatriaxōnālis: a diagonal moving in three axes at once.

(dia)tetraxonal diatetraxōnālis: a diagonal moving in four axes at once.

4-polytopes

Platonic polychora

All of these are agreed upon standards for the -choron suffix.

! pentachoron pentachōron: the 5-cell/4-simplex.

! tesseract/octachoron tesseractīs/octachōron: the 8-cell/4-cube. Tesseract for the regular octachoron.

! hexadecachoron hexadecachōron: the 16-cell/4-orthoplex.

! icositetrachoron icositetrachōron: the 24-cell.

! hecatonicosachoron hecatonicosachōron: the 120-cell.

! hexacosichoron hexacosichōron: the 600-cell.

Other

! glome glomus: a 3-sphere (4D sphere). Combining form glomer-, resulting in adjective glomeral.

semiglome sēmiglomus: a glome cut in half by a realm.

! gongyl gongylus: a 4-ball (filled glome). Adjective gongylic.
Disputed between "gongol" and "gongyl". In my opinion, "gongyl" is the more correct term as it accurately reflects its origin from Latin gongylus.

glomeroid glomeroīdēs: a 3-ellipse (the 4D equivalent of an ellipsoid.
Theoretically, a glomeroid should, as an analogy with spheroid, be a glome squashed on only one axis. However, as there isn't really another good word for a 4D ellipse, glomeroid here simply means any 3-ellipse.

5-polytopes

Platonic polytera

! hexateron hexateron: the 5-simplex.

! penteract/decateron penteractīs/decateron: the 5-cube. Penteract for the regular decateron.

! triacontaditeron triacontaditeron: the 5-orthoplex.

Other

phennion phennion: a 4-sphere (5D sphere). Plural phennia, adjective phennic.

hemiphennion hēmiphennion: a phennion cut in half by a flune.

phenind pheninda: a 5-ball (filled phennion). Adjective phenindic.

jaguar onca: the ((III)(II)) toratope.

≥6-polytopes

leopard (leo)pardus: the ((II)(II)(II)) toratope.

lion leō: the ((III)(III)) toratope.

Directions

Spatial

dysme–anatole dysmē–anatolē: direction perpendicular to north/south, east/west, and up/down, usually corresponding to the W axis (anatole is +W, dysme is -W).

borras–notos borrās–notos: direction perpendicular to anatole/dysme in the 5th dimension, usually corresponding to the V axis (notos is +V, borras is -V).

Relative

! on–gain ana–cata: the directions perpendicular to front/back and left/right. In clockwise order it goes: on, right, gain, left.

! surn–dorn surnus^&–dornus^&

Lengths

! breadth amplitūdō: broad amplus: the length corresponding to the wint/zant direction.

Rotations (Euler angles)

The 3D rotations (pitch, yaw, roll) were included here for reference. The 4D rotations were taken from the game Moena, while the 5D ones were taken from various sources (specifically this message by PlanetN9ne in the 4D Miner Discord server, a game where saying it's actually 5D is a major spoiler, and my own addition of topple).

Since I couldn't find the Latin terms for the 3D rotations, they are left blank. Some were inspired by Romance language's translations (specifically Portuguese).

! pitch: rotation around the top–front plane (turning up/down).

! yaw: rotation around the front–right plane (turning left/right).

! roll: rotation around the top–right plane.

! reel: rotation around the front–on plane (turning on/gain).

! twirl: rotation around the right–on plane.

! tumble: rotation around the top–on plane.

coil: rotation around the front–surn plane (turning surn/dorn).

gnarl: rotation around the right–surn plane.

! whirl: rotation around the on–surn plane.

topple: rotation around the top–surn plane.

Planets

For a planetary coordinate system that makes the most sense, Hopf coordinates are used, since they make double rotations very natural.

There are two types of rings (equators): the solar equator (or simply equator) refers to the ring closest to the ecliptic (path of the Sun across the celestial glome), while the polar equator (or simply pole) is the opposite ring to the solar equator. Due to double rotation, both can have independent rotation speed.

rupiglome rūpiglomus: the region of a glome with latitude above or below 45°. The south rupiglome is the half closer to the solar equator (φ<45°), while the north rupiglome is the half closer to the polar equator.
Not to be confused with the semiglome; the semiglome has the boundary of a half glome while the rupiglome has the boundary of a Clifford torus.

Coordinates

latitude lātitūdō: distance from the solar equator (φ). Goes from 0° (equator) to 90° (pole).

longitude longitūdō: the coordinate along the solar equator (λ). Runs through an entire circle (goes from 0 to 2π). Is not defined for the polar equator (φ=90°).

colongitude colongitūdō: the coordinate along the polar equator (χ). Runs through an entire circle (goes from 0 to 2π). Is not defined for the solar equator (φ=0°).

line meridian merīdiānus līneāris: varying latitude, has the form of a line.

line parallel parallēlus līneāris: varying longitude, has the form of a circle (or point at φ=90°).

line coparallel coparallēlus līneāris: varying colongitude, has the form of a circle (or point at φ=0°).

parallel parallēlus: constant latitude, has the form of a Clifford torus along the equators.

meridian merīdiānus: constant longitude, has the form of a great hemisphere (plane taking half the area of the glome)

comeridian comerīdiānus: constant colongitude, has the form of a great hemisphere.

Cardinal directions

west–east: measure along longitude, east points towards the rotation of the solar equator.

dysme–anatole dysmē–anatolē: measure along colongitude, anatole points towards the rotation of the polar equator.

south–north: measure along latitude. South is repurposed to be "equatorwards" and north "polewards".

Quantities and units

! 4-volume: bulk B oncus: Measured in quartic length (e.g. m⁴).

! 3-surface: surcell volume V volūmen supercellae: Included twice for completeness. Measured in cubic length (e.g. m³)

3-angle: spatial angle Ψ angulus spatiālis: 4D equivalent of the solid angle.
Its main units would be the choradian (cr), equivalent to 1/2π² ≈ 0.05066059 of the glome, and the cubic degree (deg³), which equals 5832000/π³ ≈ 1/188090.9 choradians. The whole glome has 2π² ≈ 19.7392 cr or 11664000/π ≈ 3712767 deg³.

Physics

There were included to compare between 3D and 4D physics units.

! 4-density: dimension ML⁻⁴ (kg/m⁴): 4D equivalent of density. Taking the physics of our Universe and extrapolating them to 4D, densities seem to be on the order of 10¹² kg/m⁴.
This result was obtained by taking the molar volume of water, 3.35×10²⁸ molecules per cubic meter, exponentiating it to get 1.08×10³⁸ molecules per quartic meter, and multiplying by the molar mass of water 0.018 kg/mol, obtaining 3.22×10¹² kg/m⁴.

! 4-pressure: dimension ML⁻²T⁻² (kg·m⁻²·s⁻², N/m³): 4D equivalent of pressure. Since 3D pressure is force over area (N/m²), then 4D pressure is force over volume (N/m³).

! 4-gravitational constant: dimension M⁻¹L⁴T⁻² (kg⁻¹·m⁴·s⁻², N·m³·kg⁻¹): 4D equivalent of the gravitational constant, assuming 4D gravity has a cubic falloff (F∝r⁻³)
To prove the dimension, we can use F=GMm/r³. Rearranging for G, we get G=Fr³/Mm. Since F has dimension MLT⁻², then the expression could be written as x=MLT⁻²L³M⁻². Multiplying it all, we get x=M⁻¹L⁴T⁻².
In fact, the n-gravitational constant has dimension M⁻¹LⁿT⁻².