This made more sense to me than the model we had in class, and it still had a triangular prism and a triangular pyramid, but it had a rectangular pyramid instead of a square pyramid. From here, as a continuation of my daily work, I decided to draw the nets of each piece and actually construct the figure and see if it would work.
I started with the net of the triangular prism (the one in the top left corner in the image above). I first started by drawing smaller nets that were to-scale of the actual figure I was going to create, I used the scale were 6cm = 1 4/10cm, and (72)^(1/2)cm = 2cm. I visually pulled the each triangular base flat first, and the I knew the square their bases were attached to was the 6cm x 6cm square face of the cube. I then visually unraveled the sides of the prism and laid it out flat. So my smaller scale version the net of the triangular prism looked like this:
Lastly, I had to make the smallest and trickiest piece. I knew that the base of the triangular pyramid would lay on the equilateral triangle from the rectangular pyramid, so the base was an equilateral triangle with side lengths of (72)^(1/2)cm. It made it simple from there because I knew that each side of the base was going to be the hypotenuse of the triangles creating the sides. However, it was very tricky because again I had to make sure that were the 6cm sides met was a 90 degree angle. To make sure, I erected a perpendicular line from the midpoint of each side of the equilateral triangle. This created a line for the two 6cm side lengths to meet to ensure that they created a 90 degree angle. This is what I came up with for the net of the triangular pyramid:
Once I got the nets sketched that were to-scale, I made the bigger nets and folded each piece of the cube. Here are the 3 separate piece after I folded and taped them:
They all turned out fairly well and fit together! Here is the succession of adding each piece:
And the final product!
It kind of looks like the pieces didn't all fit perfectly in the picture, but that is because of my taping abilities. They really did fit snugly when I held them.
Overall, from this, I felt like this reinforced the idea that there isn't only one way to do things. I think it was challenging trying to come up with a different way to make the pieces that still works and fits together. I am also very satisfied that I did do this because I became a lot less frustrated knowing that the way I was trying to construct it and was thinking about it in class really did work!