User:EricABQ/Glossary

Coordinate terms across dimensions
Many terms used in the polytope community are parts of patterns that cross dimensions.

These are the terms I use, but most of them are standard in the community, at least to the degree that the ideas are discussed at all. The terms that aren't common words originated from a variety of sources, including Jonathan Bowers' and George Olshevsky's multidimensional glossaries, and the hi.gher.space glossary.

Polytopes

 * General: polytope
 * 0D: point
 * 1D: polytelon
 * 2D: polygon
 * 3D: polyhedron
 * 4D: polychoron
 * 5D: polyteron
 * 6D: polypeton
 * 7D: polyexon/polyecton
 * 8D: polyzetton
 * 9D: polyyotton
 * 10D: polyxennon/polyronnon (?)
 * 11D: polydakon/polyquetton (?)
 * This system has been extended up to 10^45 dimensions.

Elements of polytopes

 * General: element
 * 0D: vertex
 * 1D: edge
 * 2D: face
 * 3D: cell
 * 4D: teron
 * 5D: peton
 * 6D: ecton/exon
 * 7D: zetton
 * 8D: yotton
 * 9D: xennon/ronnon (?)
 * 10D: dakon/quetton (?)
 * This system has been extended up to 10^45 - 1 dimensions.

Hyperspheres

 * General: hypersphere
 * 1D: circle
 * 2D: sphere
 * 3D: glome
 * 4D: pentorb/pentasphere
 * 5D: hexorb/hexasphere

Hyperspheres

 * General: hyperball
 * 1D: dyad/line segment
 * 2D: disk
 * 3D: ball
 * 4D: gongyl/gongol
 * 5D: pentaball

Hypersurfaces

 * General: hypersurface/surtope (but note that this is different from Wendy's use of "surtope" because it can apply to curved objects)
 * 1D: boundary (I haven't seen this in a multidimensional glossary but it sounds like the obvious term)
 * 2D: surface
 * 3D: surcell
 * 4D: surteron

Flexible n-D objects in (n+1)-D space
Note: the dimension refers to the dimension of the object.

These terms are from hi.gher.space. They correspond to Wendy's hedrix, chorix, etc.


 * 1D: string
 * 2D: sheet
 * 3D: swock

Cardinal directions in nD
These are defined in terms of planet rotation. The terms "marp" and "garp" were invented by Jonathan Bowers.


 * 2D: east/west
 * 3D: north/south
 * 4D: marp/garp