When rotating shapes, vertices are just slightly off

Question

I'm working on a manim challenge from this video: https://youtu.be/HKPm8FZYaqI?t=700. The challenge is to code the animation which starts at 11:40 and ends at 11:49.

I got up to the point where the triangles are rotated and copied over to the second square, but for some reason they are just the ones that I had to rotate are just ever so slightly off, while the ones I didn't have to rotate seem to be perfect.

Look at this image:

The triangles fit perfectly inside the square to the right. But in the right square, the ones that were rotated (1 and 4) do not. Below is a closeup of what I mean for triangle number 1:

Of course, this is how I want it to look: The dimensions of the shapes and maybe the colours are a little different, but that is because this is the solution of the author of the video, and the previous was my attempt. I don't care about that, I only care about why the triangles don't fit perfectly in my attempt like they do here. Zooming in on this picture, we see that the triangles do indeed fit perfectly:

Any insight into why this is happening would be very much appreciated!

The source code for my animation is this:

class Pythagoras(Scene):
    def construct(self):
        title = TextMobject("Pythagorean Theorem")
        title.to_edge(UL)

        pre_square = Polygon(
            [-2, 2, 0],
            [2, 2, 0],
            [2, -2, 0],
            [-2, -2, 0],
            color=WHITE
        )

        self.wait()


        square2 = Polygon(
            [-1.41, 1.41, 0],
            [1.41, 1.41, 0],
            [1.41, -1.41, 0],
            [-1.41, -1.41, 0]

        )
        square2.rotate(PI/6)

        triangle1 = Polygon(
            [-2, 2, 0],
            [-2 + math.sqrt(6), 2, 0],
            [-2, 2 - math.sqrt(2), 0],
            color=YELLOW
        )

        triangle2 = Polygon(
            [2, 2, 0],
            [-2 + math.sqrt(6), 2, 0],
            [2, 2 - math.sqrt(6), 0],
            color=YELLOW
        )

        triangle3 = Polygon(
            [2, 2 - math.sqrt(6), 0],
            [2, -2, 0],
            [2 - math.sqrt(6), -2, 0],
            color=YELLOW
        )

        triangle4 = Polygon(
            [-2, 2 - math.sqrt(2), 0],
            [-2, -2, 0],
            [2 - math.sqrt(6), -2, 0],
            color=YELLOW
        )

        triangles = [triangle1, triangle2, triangle3, triangle4]
        for triangle in triangles:
            triangle.set_fill(YELLOW, 0.6)

        self.play(Write(title), ShowCreation(pre_square), ShowCreation(triangle1), ShowCreation(triangle2), ShowCreation(triangle3), ShowCreation(triangle4))

        self.wait()

        group = VGroup(pre_square, triangle1, triangle2, triangle3, triangle4)

        self.play(ApplyMethod(group.to_edge, LEFT, {"buff": 1.6}))
        self.wait()

        square3 = pre_square.copy()

        self.play(ApplyMethod(square3.shift, RIGHT * 7))

        triangle2.generate_target()
        triangle2.target.shift(RIGHT * (7- math.sqrt(6)))

        triangle1.generate_target()
        triangle1.target = triangle2.target.copy().rotate(PI) 

        triangle3.generate_target()
        triangle3.target.shift(RIGHT * 7)

        triangle4.generate_target()
        triangle4.target = triangle3.target.copy().rotate(PI)


        self.play(MoveToTarget(triangle1.copy()), MoveToTarget(triangle2.copy()), MoveToTarget(triangle3.copy()), MoveToTarget(triangle4.copy()))

        self.wait()

Answer 1

The problem is the thickness of the VMobjects, by default it is 4, if you change it to 2 or 1 (in the solution that I give is 1) those corners are removed. Add this in your for:

        for triangle in triangles:
            triangle.set_fill(YELLOW, 0.6)
            triangle.set_stroke(None,1.5)
            #or
            #triangle.set_stroke(width=1.5)
            #it is the same