AMS Crossword

5. A hexagon is a hexagon inscribed in a reference triangle that has sides which are alternately parallel and antiparallel to the corresponding sides of the triangle.
6. Theorem that says the internal (external) bisecting plane of a dihedral angle of a tetrahedron divides the opposite edge in the ratio of the areas of the adjacent faces.
7. Dog on a leash
8. Average distance between two points chosen at random in cube line picking
9. A prime number of the form 2^n-1

1. The first one of these of a tile is the set of all tiles that have a common boundary point with that tile (including the original tile itself)
2. The curve a hanging flexible wire or chain assumes when supported at its ends and acted upon by a uniform gravitational force.
3. Theorem that says If A is a unital Banach algebra where every nonzero element is invertible, then A is the algebra of complex numbers (one of the names)
4. 10^(42)
10. A certain graph on 1782 vertices