I invite you to fold these two classic and clever Tomoko Fuse boxes with me! They have remained an inspiration to me since I started folding. I encourage you to try these models even if you are a relatively inexperienced folder and might consider them over your head. I will go slowly so that you can experience the satisfaction of making something that might be a stretch for you. I will also point out some mathematical connections as we fold, especially for teachers who might want to use these ideas with students. Nesting the triangle box bottoms is my new project, and sizing them properly is the adventure. You will learn how to do that even if you don’t finish all of them. Students can expect to have finished a hexagon box and a triangle box by the end of class. Having the proper paper ready is essential.
Origami Boxes by Tomoko Fuse. ISBN: 0-87040-921-6. pp 55-72. I believe this book is out of print, and I don't know if the models are published in other books.
Hexagon box bottom and top: 12 squares + one extra sheet to make a template: 15 cm (6 inch) recommended, bigger is fine. Smaller is fine if you are an experienced folder. Duo paper is great for the top (6 squares) because the back will show. The back will not show for the bottom. Kami or light weight duo are good choices for paper since there are multiple layers of paper in the finished box. Heavier paper could be problematic.
Triangle box bottom and top: 6 squares: 15cm (6 inch) or larger is fine just for learning the box.
If you want to make triangle boxes that nest in the hexagon box as shown, you need 3 squares for each box bottom (so a total of 18 squares) that are 1/2 the side length you used for the hexagon box. For example, if you used 15 cm (6 inch) for the hexagon box, you need 18 squares of 7.5 cm paper (3 inch). You will be modifying these squares in order to nest, so you will need an extra square to make a template and a cutting tool. Kami is a good choice. Heavier paper could be problematic.
We probably will not finish all 6 of the nesting triangle box bottoms during class, but you will know how to complete the project.