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.
(dia)pentaxonal: moving in five axes at once, "pentagonal"
(dia)tetraxonal: moving in four axes at once, "tetragonal"
(dia)triaxonal: moving in three axes at once, "triagonal"
anatole: (hypergeography) cardinal direction of positive colongitude, perpendicular to east, west, north and south and opposite to dysme
anst: (hypergeography) short form of anatole
anstward: (hypergeography) towards anatole
artitude: (hypergeography) equatorial latitude, perpendicular to latitude. Symbol ψ
borras: (hypergeography) cardinal direction of positive artitude, perpendicular to east, west, north, south, anst and dyst and opposite to notos
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 χ
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
dysme: (hypergeography) cardinal direction of negative colongitude, perpendicular to east, west, north and south and opposite to anatole
dyst: (hypergeography) short form of dysme
dystward: (hypergeography) towards dysme
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 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
notos: (hypergeography) cardinal direction of negative artitude, perpendicular to east, west, north, south, anst and dyst and opposite to borras
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 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 most perpendicular to the ecliptic
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 most parallel to the ecliptic
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
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