A glossary of my preferences for superdimensional (≥4D) vocabulary. There aren't really too many stardards set in place, so you can kind of make up whatever you want for now...
This was partly inspired by Hi.gher.space's Multi-dimensional glossary.
An older revision of this page can be found here.
Key:
green terms are 4D;
yellow underlined terms are 5D;
(dia)pentaxonal: moving in five axes at once.
(dia)tetraxonal: moving in four axes at once.
(dia)triaxonal: moving in three axes at once, "triagonal".
Clifford torus: the Cartesian product of two circles.
anst: (hypergeography) cardinal direction of positive colongitude, opposite to dyst
anstward: (hypergeography) towards anst
artitude: (hypergeography) 90° latitude, symbol χ
breadth: horizontal measure, perpendicular to length and width
broad: great adjective of breadth
coil: rotation in the front-surn plane.
colongitude: (hypergeography) the longitude running along the polar ring, perpendicular to longitude. Symbol λ
demipenteract: the 5D Archimedean solid bound by 10 hexadecachora and 16 pentachora, the 5-demicube.
dorn: horizontal personal direction, perpendicular to left, right, on and gain and opposite to surn.
dornward: towards dorn.
dyst: (hypergeography) cardinal direction of negative colongitude, opposite to anst.
dystward: (hypergeography) towards dyst.
gain: horizontal personal direction, perpendicular to left and right and opposite to on.
gainward: towards gain.
glome: 3-sphere, the set of all points with a fixed radius from some center in R4 space.
gnarl: rotation in the right-surn plane.
gongyl: 4-ball, the set of all points at or below a fixed radius from some center in R4 space. That is, a filled version of the glome.
hecatonicosachoron: the 4D Platonic solid bound by 120 dodecahedra, the 120-cell.
hemiphennion: a phennion sliced in half by a 4D plane.
hexacosichoron: the 4D Platonic solid bound by 600 tetrahedra, the 600-cell.
hexadecachoron: the 4D Platonic solid bound by 16 tetrahedra, the 16-cell.
hexateron: the 5D Platonic solid bound by 6 pentachora, the 5-simplex.
icositetrachoron: the 4D Platonic solid bound by 24 octahedra, the 24-cell.
jaguar: the ((II)(III)) toratope.
kirn: (hypergeography) cardinal direction of positive artitude, opposite to thern.
on: horizontal personal direction, perpendicular to left and right and opposite to gain.
onward: towards on.
pentachoron: the 4D Platonic solid bound by 5 tetrahedra, the 5-cell.
penteract: the 5D Platonic solid bound by 10 tesseracts, the 5-cube.
phenind: 5-ball, the set of all points at or below a fixed radius from some center in R5 space. That is, a filled version of the phennion.
phennion: 4-sphere, the set of all points with a fixed radius from some center in R5 space.
polar ring: (hypergeography) the ring of rotation farthest from the ecliptic plane.
quartolume: 4D equivalent of volume, dimension L4.
quintolume: 5D equivalent of volume, dimension L5.
reel: rotation in the front-on plane.
rupiglome: (hypergeography) a glome sliced by a Clifford torus, leaving a toroidal half.
semiglome: a glome sliced in half by a 3D plane.
solar ring: (hypergeography) the ring of rotation closest to the ecliptic plane.
surn: horizontal personal direction, perpendicular to left, right, on and gain and opposite to dorn.
surnward: towards surn.
tesseract: the 4D Platonic solid bound by 8 cubes, the 4-cube/8-cell.
thern: (hypergeography) cardinal direction of negative artitude, opposite to kirn.
topple: rotation in the up-surn plane.
triacontaditeron: the 5D Platonic solid bound by 32 pentachora, the 5-orthoplex.
tumble: rotation in the up-on plane.
twirl: rotation in the right-on plane.
whirl: rotation in the on-surn plane.