Hypersphere[]
A hypersphere is a generalisation of the circle and sphere to higher dimensions. An X-dimensional hypersphere consists of the locus of all points equidistant from another point in X-dimensional space.
Hypercube[]
A hypercube is the same object as a hypersphere, except it is a generalisation of the square and cube to higher dimensions.
| Zeroth | First | Second | Third | Fourth | Fifth | Sixth | Seventh | Eighth | Ninth | Tenth | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Simplex | Point | Line | Triangle | Tetrahedron | Pentachoron | Hexateron | Heptapeton | Octaexon | Enneazetton | Decayotton | Hendecaxennon |
| Hypercube | Point | Line | Square | Cube | Tesseract | Penteract | Hexeract | Hepteract | Octeract | Enneract | Dekeract |
| Cross | Point | Line | Square | Octahedron | Hexadecachoron | Pentarss | Hexarss | Heptarss | Octarss | Ennearss | Decarss |
| Hypersphere | Point | Line | Circle | Sphere | Glome | Hyperglome | Hexaphere | Heptaphere | Octaphere | Enneaphere | Decaphere |