Angle between lines drawn from 4-simplex vertices to its center For triangle, the angle between lines drawn from vertices to its center is 120 degrees.
I have already read the answer to question
Angle between lines joining tetrahedron center to vertices
and there the angle is approximately 108,5 degrees
I am principally interested to know what happens in 4-dimensional case, what's the angle there? I have a hypothesis for an interaction model in 4D, and would appreciate an answer as it allows me to calculate whether the hypothetical  structure is going to be stable or decay because of its constituents. 
No need to answer this, but out of curiosity: I understand simplexes exist in even higher dimensions, so when the number of dimensions increases, is the angle going only nearer and nearer to 90 degrees, or even below it? Is there a generic formula to this?
 A: Think of an equilateral triangle with vertices at unit distance from the center.  If you draw vectors from the center to the vertices then by symmetry the resultant must match a rotation of itself, possible only for zero resultant.  Also by symmetry if you pick one vector the components of every other vector along your chosen one must be the same.  In your triangle the second and third vectors must therefore have components of $-1/2$ to be equal to each other and give a zero resultant for all vectors.  The angle between two unit vectors where one has a component of $-1/2$ along the other is then $\cos^{-1}(1/2)=120°$.
When you apply this idea to an $n$-dimensional simplex the angle works out to $\cos^{-1}(-1/(n-1))$, which for large $n$ approaches but never reaches a right angle.
A: It’s been a while since I was participating a geometry class, and that must have been in high school.  While this has probably popped up there, can’t recall anything about this at the university. 
Not essential for physics degree, probably of practical use in architecture or whatnot.
Anyway: that you mention the reasoning, it’s obvious and calculation yields about 104,5 degrees 
Thanks, this resolved the question. And gave the answer for the general rule as well
