Dissection Pieces

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Origami Dissection Puzzles

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

Index

The Pieces

TetrahedronPyramidcube with two pyramids sliced off cube (container for several pieces)Octahedron

How they fit together

Puzzle 1Puzzle 2Puzzle 3

The piecesPyramid

1. Take a square and fold thus:

https://www.math.lsu.edu/~verrill/origami/disect/#cube

https://www.math.lsu.edu/~verrill/origami/disect/#tet

https://www.math.lsu.edu/~verrill/origami/disect/dis2.jpg




https://www.math.lsu.edu/~verrill/origami/disect/#P3



https://www.math.lsu.edu/~verrill/origami/disect/#oct

https://www.math.lsu.edu/~verrill/origami/disect/#cube

https://www.math.lsu.edu/~verrill/origami/disect/#slice

https://www.math.lsu.edu/~verrill/origami/disect/#pyr

https://www.math.lsu.edu/~verrill/origami/disect/#tet






2. Fold over the three corners asshown; the angle folded over shouldbe 15 degrees, just guess, make it sothat the angle folded looks the sameas the angle between the edge of thepaper and the diagonal creases.

3. Fold points a and btogether thus:

4. fold point e under flapd, d under c, c under ethus:

5. Finally foldflap g underflap e also:

Another view of the finishedpyramid:

Tetrahedron

1. Make crease marks half way along theedges:

2. fold a diagonal between two half marks.Make crease marks marking 1/4 marks;make these about half way to the diagonalfold:

3. This fold is made as the next digaram

4. The other 60 degreecrease is formed in a





shows,.

similar way, by makingpoint b touch crease c.

5. Fold points g and h to the creases, toform a diagonal crease through theintersection of the 60 degree creases:

6. Turn over:

7. Fold along the 60 degree crease thus:8. Fold the edge bs, folding over thediagonal crease underneath:

9. Fold the other side similarly, and thenturn over:

10. Make two pieces and put them together:





Flaps and pockets go into flaps andpockets, marked with "p" and "f":

Fold so that pockets, flaps, etc, are all"outside": (This shows model using onesheet of paper that's yellow on one sideand red on the other, and the other sheet of paper is green on one side and blue on theother.)

With the colours asdescribed, you getsomething 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 coloureven 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"; onepossibility is simply to make another of the pyramids, and turn it upside down and place it in thetriangular 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 belowshow how it should look from the front, and from below, and how it should not look; there is atendency that it might look like the third picture, but if you fold acurately, it should be OK; also keepingother 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 haveby 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 anoctahedron via the "tetra-unit". The Tetraunit is much more versitile than the unit used for thetetrahedron above; however, the above unit uses far fewer folds, so is faster to make, and also has largervolume for the same size paper. Anyway, if you want to make an octahedron to fit with four of thetetrahedra 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 paperfor the tetraunit models:

How the pieces fit together

Puzzle One

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.)

https://www.math.lsu.edu/~verrill/origami.html





Puzzle Two

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

Puzzle Three

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.)

Dissection Pieces

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