How to generate the n-simplex? I was following this wikipedia section, in the simplex article to see if I could create a MATLAB algorithm to generate a simplex with $n$ points in $3$-dimensional space.
Sure enough it works for 4 vectors. The section also says that alternating between the two methods described, one can generalize for any number of vectors (or even dimensions). Thing is, I don't see how that is possible.
Consider $n > 4$, for example 6. Following the method, the fifth and sixth vector would have the same first and second coordinate as vector 3 and 4. One would then use the dot product rule to find the 3rd coordinate for both. In other words, vectors 5 and 6 are identical.
Am I interpreting the algorithm wrong?

Note that the $n$-simplex as constructed in the wikipedia section is a subset of $\mathbb R^n$, so to construct the six corners of the $5$-simplex, you need Matlab vectors of length $5$.
