Editing Regular polytope (section)

===Regular simplices===
{|class="wikitable" align="right" style="border-width:30%;"
|+ Graphs of the 1-simplex to 4-simplex.
|align=center|[[Image:1-simplex t0.svg|80px]]
|align=center|[[Image:2-simplex t0.svg|80px]]
|align=center|[[Image:3-simplex t0.svg|80px]]
|align=center|[[Image:4-simplex t0.svg|80px]]
|-
| [[Line segment]]
| [[Equilateral triangle|Triangle]]
| [[Tetrahedron]]
| [[Pentachoron]]
|-
| &nbsp;
| [[Image:Regular triangle.svg|80px]]
| [[Image:Tetrahedron.svg|80px]]
| [[Image:Schlegel wireframe 5-cell.png|80px]]
|}
{{main|Simplex}}

These are the '''regular simplices''' or '''simplexes'''. Their names are, in order of dimension:

:0. [[Point (geometry)|Point]]
:1. [[Line segment]]
:2. [[Equilateral triangle]] (regular trigon)
:3. Regular [[tetrahedron]] (triangular pyramid)
:4. Regular [[pentachoron]] ''or'' 4-simplex
:5. Regular [[hexateron]] ''or'' 5-simplex
:... An ''n''-simplex has ''n''+1 vertices.

The process of making each simplex can be visualised on a graph: Begin with a point ''A''. Mark point ''B'' at a distance ''r'' from it, and join to form a [[line segment]]. Mark point ''C'' in a second, [[orthogonal]], dimension at a distance ''r'' from both, and join to ''A'' and ''B'' to form an [[equilateral triangle]]. Mark point ''D'' in a third, orthogonal, dimension a distance ''r'' from all three, and join to form a regular [[tetrahedron]]. This process is repeated further using new points to form higher-dimensional simplices.