[jonahx]

https://en.wikipedia.org/wiki/Simplex

Common for visualizing mixtures of three things!

[vl]

While you are technically correct, since any triangle is a simplex, this is not relevant to this visualization.

For this visualization: get positive quantities in 3D space, normalize to 1, now you have dot on a triangle on 1-sphere in a positive octant. Project triangle into 2D space a this is your visualization.

[Paracompact]

2-sphere, I believe you mean to say.