# Origami Dissection Puzzles

By a dissection puzzle, I mean the kind of puzzle where you have several polyhedra, and you have to fit them together to make another. There are lots of simple examples, and then more difficult puzzles. For now I only have simple puzzles; but although they are simple they are still fascinating.

## Index

The Pieces

How they fit together

## The pieces

### Pyramid

 1. Take a square and fold thus: 2. Fold over the three corners as shown; the angle folded over should be 15 degrees, just guess, make it so that the angle folded looks the same as the angle between the edge of the paper and the diagonal creases. 3. Fold points a and b together thus: 4. fold point e under flap d, d under c, c under e thus: 5. Finally fold flap g under flap e also: Another view of the finished pyramid:

### Tetrahedron

 1. Make crease marks half way along the edges: 2. fold a diagonal between two half marks. Make crease marks marking 1/4 marks; make these about half way to the diagonal fold: 3. This fold is made as the next digaram shows, by making point a touch crease at d. 4. The other 60 degree crease is formed in a similar way, by making point b touch crease c. 5. Fold points g and h to the creases, to form a diagonal crease through the intersection of the 60 degree creases: 6. Turn over: 7. Fold along the 60 degree crease thus: 8. Fold the edge bs, folding over the diagonal crease underneath: 9. Fold the other side similarly, and then turn over: 10. Make two pieces and put them together: Flaps and pockets go into flaps and pockets, marked with "p" and "f": Fold so that pockets, flaps, etc, are all "outside": (This shows model using one sheet of paper that's yellow on one side and red on the other, and the other sheet of paper is green on one side and blue on the other.) With the colours as described, you get something like this:

Note, it's not too hard to do a little reversing and rearranging of some of the folds (making no additional creases) so that only one side of each sheet of paper shows, so you can make a model of a single colour even if your paper is white on one side, coloured on the other.

### cube with two pyramids sliced off

Note, this ends up looking like a kind of box; there are various methods to make it more "solid"; one possibility is simply to make another of the pyramids, and turn it upside down and place it in the triangular openning of this "box".

### cube box

 1. First fold the paper thus: 2. open up from point p as shown. views from above and the front are shown. 3. Make four identical pieces, and fit them together, the flap of one fitting into the pocket of the next. This is a little bit tricky; to get the last one to work properly may need some practice. The figures below show how it should look from the front, and from below, and how it should not look; there is a tendency that it might look like the third picture, but if you fold acurately, it should be OK; also keeping other pieces inside it will stop it falling in on itself.

Note, this box is influenced by Fuse designs - it's not the same as any of her boxes in the books I have by her; I appologise if it is the same as some other by Fuse. Anyway, I recommend Fuse origami books - she has a lovely collection of modular boxes, much more elegantly constructed than this one.

### Octahedron

I am working on making a better octahedron, but one possibility, which fits into the scheme here (sizewise), is to take a piece root two times as large as the other pieces of paper, and use it to make an octahedron via the "tetra-unit". The Tetraunit is much more versitile than the unit used for the tetrahedron above; however, the above unit uses far fewer folds, so is faster to make, and also has larger volume for the same size paper. Anyway, if you want to make an octahedron to fit with four of the tetrahedra on this page, take paper with ratios like this:

This above means the small size is obtained from the large size by removing the corners.

An alternative method is to use squares from A5 paper for the models on this page, and from A4 paper for the tetraunit models:

## How the pieces fit together

Take four of the pyramids, and one of the tetrahedra, and put them all into the box. (all the pieces of paper used are the same size, so needs 10 squares of paper, all the same size.)

Take four tetrahedra, and put them into one tetrahedra made from a peice of paper twice the size, together with an octahedron.

Take two pyramids, and the shape I call "cube with pyramids sliced off", and fit them all into the cube. (All pieces of paper the same size.)