Tetrahedrons
My puzzle coffer is low. I've a few submissions to read through. So
here are a few quick problems for you.
On a regular tetrahedron of sidelength 1:

From the midpoint of one edge, two lines are
drawn along the surface to the two edgemidpoints of one side. What is
the angle between these lines?

From the midpoint of one edge, two lines are
drawn along the surface to the edgemidpoints of different sides. What is
the angle between these lines?

What is the farthest surface distance possible between any two points?

What is the shortest distance between two nonadjacent edges?

Remove one tetrahedron from each corner, each with sidelength of 1/2.
For the figure created:
 What is it called?
 Connect two opposite vertices via the shortest surface line. What is
the angle formed by this line?
 Each of the removed tetrahedra were 1/8 the volume of the large one.
How many more 1/8 tetrahedra can be cut from the remaining figure,
in no more than one piece each?
If you know of other good questions to add to this list, send them.
I'll add them as their received.
Source: Original, though influenced by many past readings.
Solution
Mail to Ken