I find the mathematical naming system for polyhedra to be somewhat cumbersome, especially when the full and precisely accurate term is used. According to the text book definition this box is officially a form of sunken rhombicuboctahedron. A slightly less complicated version identifies it as a cantellated cube or cantellated octahedron. I prefer to refer to the model simply by its general class name: an octahedron.
It has eight faces around its sagital plane and eight faces around its coronal plane.
But now we are getting complicated again. The neurological terms are just as confusing to the average Jill or Joe as the formal mathematical terms.
The original version of the box divides the rim of the lid in half so that the model appears to be in two equal halves when closed.
A fan prefers to make the box without turning the rim over. (See the red box which she folded.) It makes for a less bulky lid which is useful when the box is made from thicker paper.
For text weight paper use two squares, one about half an inch smaller than the square which will be used for the lid. I use one 8-1/2 inch square and one 8 inch square. It works rather well in Stardream paper which is 81 lb text weight.
The model works in other weights as well. The white and gold box was made from light weight pearlized text paper on the bottom (about 60lb text) and even thinner velum for the top. I generally try to avoid using velum as it is somewhat brittle and has a nasty tendency to crack, especially in areas where it is stressed or the crease is folded and unfolded regularly.
Izumi, the woman who made the red full rimmed version, is Japanese. She married a Mexican friend of mine and now speaks fluent Mexican Spanish.
She teaches the Japanese language to Mexican locals. In her teaching area she displays a vase of paper flowers which I folded from traditional patterns when I stayed in that house a couple of years ago.
The irony is that, although Japanese, Izumi could not show her students how to fold these models because she was almost entirely ignorant of her native art. She begged me to teach her while I was there this time.
Believe me, it felt very strange teaching a native born Japanese how to fold origami models.
She turned out to be a very good student. When I woke the morning after I taught her to fold the octahedron box I was amazed to discover the table littered with increasingly sophisticated models. Unfortunately most of my photos of her models were blurry or they would have been displayed proudly on this blog.
Fortunately her face was in focus, and here she is displaying two of her newly learned and folded models.
Way to go, Izumi! Buen trabajo!
Here is the crease pattern. The green shaded areas are hidden when the model is finished.
