##### Across

**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

##### Down

**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