One way to change a model design is by grafting, that is by inserting extra paper into its crease pattern. We will see possible ways to graft the blintz and how this leads to a longer masu box.
The Masu Box
“Masu” is a Japanese word for measurement, and wooden masu boxes are traditionally used in Japan for measuring rice.2 The literal translation would then be “measurement box.”
As an origami model, it has become known as the masu box, a phonetic translation of マス, used in a 1931 Japanese book by Isao Honda.3 In his English “The World of Origami” (1965) Honda calls it a “box,” and states that it is of “the type for measuring rice.”4 Harbin (1956) calls it a “utility box” or “container.”5
David Mitchell observes6 that several European references are older, going back at least to 1864 where the Fröbelian-inspired Elise Calcar describes the model under the name ashtray (“Het aschbakje”).7
Thus, as with most traditional origami models, the origin is unsure, though it is useful to name it masu box as that is the widespread name today and seeing that ashtrays have gone out of fashion.
Blintzing the masu base
The masu box is a blintz model. As in the article Creating via Blintzing, we may view the masu box as “created” via blintzing the masu base.
The base is a “box” that does not lock together. The blintz provides the locking, as well as a reinforcement of the sides as the blintz effectively doubles the paper thickness.
Double-blintz the masu base to achieve a decorative effect. The excess paper from the extra blintz may be left as is, or you may experiment with decorative effects. Try it!
The masu crease pattern is simple and lends itself to variations. Indeed, Arnold Tubis and Leon Brown have a whole series of decorative boxes.8 In the rest of this article we shall see variations that appear via grafting.
Grafting Along the Medians9
In her teaching, Gay Merrill Gross introduced the terms mini-blintz and maxi-blintz.10 Instead of folding all corners to the center, you fold them to the diagonal quarter marks. Fold the corner to the closest quarter mark to get the mini-blintz, and to the farthest to get the maxi-blintz.
For the maxi-blintz, all four corners cannot be folded in at the same time without creating extra folds. Instead, fold and unfold one corner at a time, then use the creases later on.
The mini- and maxi-blintzes can be viewed as grafting extra paper into the standard blintz pattern. In the crease patterns above, the extra paper is indicated by a darker color.
The blintz and the mini- and maxi-blintzes can be seen as three instances of folding the corners along the diagonals. Marks between 0 and ½ may be called mini-blintzes, and between ½ and 1 maxi-blintzes. The standard blintz is at the ½ mark. At the mini-extreme, 0, the creases reduce to nothing; there is no folding. At the maxi-extreme, 1, we fold corner to corner. Doing the latter with all four corners and flattening gives us the square base.11
For the mini-blintz the grafting is along the medians. In the masu box this provides the excess paper that may be used for diagonal decorations. Mini-blintzes between the ⅜ marks and the 15⁄32 marks are convenient.
If, after the mini-blintz, we convert the graft into a band-pleat, and then blintz again to fold the masu box, we get the nice color change band we see in the lid above.
For the maxi-blintz the grafting is along the outer edge. In the masu box, the outer edge is positioned along the inside of the box, and there is no natural way to utilize the excess paper.
Grafting along the Diagonals
The masu crease pattern is also symmetrical in its diagonals, and we can graft these. Grafting results in a wider box with a square “hole” inside the lid where the back of the paper can be seen. Alternatively, the grafted section may be used for folding extra frills like the decorative band above. Because we have only one blintz, there is no color change this time.
Since the blintz rotates the square 45 degrees, the diagonal graft gives a median band, whereas the median graft gives a diagonal band.
The crease pattern of the masu box reveals that to obtain a longer box, we must only graft along one diagonal. Note how the grafting converts the square into an irregular hexagon. The gray triangles indicate the two possible ways to regularize the shape. By grafting the triangle corners on either two or four of the edges of that hexagon, we get back a square, or at least a rectangle, respectively.
The figure above depicts the situation where the rectangle is A4-shaped and the square is the square taken from A4. In any case, the two methods provide the same size box.
Instructions for a Longer Masu Box
1. Photo (https://commons.wikimedia.org/wiki/File:Masu,One-sho_measure,katori-city,Japan.JPG) by Katorisi, copyright CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0/) 2009. [back]
2. Masu. Wikipedia, https://en.wikipedia.org/wiki/Masu_(measurement), retrieved 2021-07-28. [back]
3. Isao Honda, Origami (Part 1) (Japan, 1931). [back]
4. Isao Honda, The World of Origami, (Tokyo: Japan Publications Trading Company, 1966), 73. [back]
5. Robert Harbin, Paper Magic (London: John Maxfield, 1956), 43. [back]
6. David Mitchell: “The Blintz Box or Masu / The Winnowing Box,” retrieved 2021-07-28 July 28, 2021, https://www.origamiheaven.com/historyoftheblintzbox.htm. David’s history site is a goldmine of verified facts on the history of origami .[back]
7. Elise van Calcar, “Kleine Papierwerkers — Wat men van een stukje papier al maken kan: Het Vouwen” (Amsterdam: K. H. Schadd, 1864) Plate 3, model number 23. [back]
8. Arnold Tubis and Leon Brown, Decorative Origami Boxes from Single Squares, Booklet 61 (United kingdom:British Origami Society 2017). [back]
9. The median is the line midway between two sides. [back]
10. Gay Merrill Gross and Nick Robinson, “Do you Speak Origami?” The Paper, 78 (OrigamiUSA: 2002) 18. [back]
11. Often called by the misleading name, “preliminary base.” [back]
12. Design and fold by Hans Dybjær. From Hans Dybkjær and Laila Dybkjær, Origami - Foldefamiliens jul (København: Papirfoldning.dk, 2010). ISBN 9-788799-235827. [back]
Other Articles in This Series
“The Complete Blintz Part 1: The Yakko”
“The Complete Blintz Part 2: History of the Blintz”
“The Complete Blintz Part 3: Blintz Story Telling”
“The Complete Blintz Part 4: The Dragon and the Might of the Blintz”
“The Complete Blintz Part 5: Creating via Blintzing”
“The Complete Blintz Part 6: The Cushion Fold”
“The Complete Blintz Part 7: Deconstructing the Corner Fold”