The left side of == is a tower of hight 3, whereas the right side is a tower of hight 4, it seems. That's what i find confusing. Do you mean:

-- tower(13, 3, 31) == 13 ^ (30 + tower(13, 2, 30)) % 31

This would match the Python test.

I noticed this comment:

    -- tower(13, 3, 31) == 13 ^ (30 + 13 ^ tower(13, 2, 30)) % 31

Why?

I'm glad you enjoyed the kata. Hopefully you solved it by your own reasoning before you found out about a "trick", and that's what's important.

Approved.

The 12 rectangles should have been:

((3, 1), (1, 0), (0, 2), (2, 3))
((4, 0), (1, 0), (1, 4), (4, 4))
((4, 0), (0, 2), (1, 4), (5, 2))
((1, 0), (0, 2), (4, 4), (5, 2))
((3, 1), (4, 0), (6, 2), (5, 3))
((1, 1), (4, 0), (5, 3), (2, 4))
((1, 1), (9, 1), (9, 4), (1, 4))
((3, 1), (5, 2), (4, 4), (2, 3))
((5, 2), (4, 2), (4, 4), (5, 4))
((9, 2), (4, 2), (4, 4), (9, 4))
((9, 2), (5, 2), (5, 4), (9, 4))
((2, 3), (5, 3), (5, 4), (2, 4))

I'll update.

The vertices are given in adjancency order, starting at any vertice and moving in either direction (i.e., clockwise or counter-clockwise). E.g.,

               (2, 1)
        (0, 2)------->(2, 3)
          |             |
  (1, -2) |             | (1, -2)
          V    (2, 1)   V
        (1, 0)------->(3, 1)

Using the dot-product, you can verify that the sides are perpendicular.

I explain it in this comment.

Thanks. Approved!

A recent Haskell translation has modified the description. Make sure this translation is not undoing those changes.

.

It's been a while since I dabbled in Scala. I see that, since then, Stream has been deprecated in favor of LazyList.

I'd rather fit the tests to the description than the description to the tests.