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Cost
$ $ $ $ $
Difficulty
• • • •
Time
3h00

Mind-Blowing Modular Origami
This is the single most time-consuming project in this book; when it was first constructed it was the largest Wire Frame modular ever made. Its polar dihedral symmetry distinguishes it from all other models in this book, as it is not based on a regular polyhedron. The name comes from its connection to planar modulars, where each plane is a assigned a letter of the alphabet. Here, the twenty-six frames represent each of the letters of the alphabet.

This model has only one paper proportion: 1:2.41. If using the template, start with relatively small squares. Rectangles ripped from 3.5" squares make a ~10" model.

Posted by Tuttle Publishing Published See Tuttle Publishing's 91 projects » © 2021 Byriah Loper / Tuttle Publishing · Reproduced with permission.
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You Will Need

  • How to fold an origami shape. The Alphabet - Step 1
    Step 1

    Making and Using the Template

    Book fold and unfold.

  • How to fold an origami shape. The Alphabet - Step 2
    Step 2

    Fold in half diagonally where shown; unfold.

  • How to fold an origami shape. The Alphabet - Step 3
    Step 3

    Fold in half between the circled areas where shown; unfold.

  • How to fold an origami shape. The Alphabet - Step 4
    Step 4

    Fold the right edge to join the intersection of the two previous folds; unfold.

  • How to fold an origami shape. The Alphabet - Step 5
    Step 5

    Fold the right edge to join the previous fold; unfold.

  • How to fold an origami shape. The Alphabet - Step 6
    Step 6

    Fold the left edge to join the previous fold.

  • How to fold an origami shape. The Alphabet - Step 7
    Step 7

    The completed template.

  • How to fold an origami shape. The Alphabet - Step 8
    Step 8

    Slide a second square into the template, so that the circled lines are flush with each other.

  • How to fold an origami shape. The Alphabet - Step 9
    Step 9

    Fold the square over along the edge of the template.

  • How to fold an origami shape. The Alphabet - Step 10
    Step 10

    Pull the square sheet out and set the template aside.

  • How to fold an origami shape. The Alphabet - Step 11
    Step 11

    Refold the crease.

  • How to fold an origami shape. The Alphabet - Step 12
    Step 12

    Mountain fold the edge to align with the top layer, and unfold everything.

  • How to fold an origami shape. The Alphabet - Step 13
    Step 13

    Rip along both lines. Keep the two equal-sized rectangles; discard the small strip on the right. Set one rectangle aside and focus on the other.

  • How to fold an origami shape. The Alphabet - Step 14
    Step 14

    Unit Preparation

    The crimp formed using the given folding method makes a 75-degree interior angle. Such units are used to make stellated polygons. The actual angle for perfectly flat polygonal frames as used here should be roughly 74.4 degrees. Using the formula (360/n+a), where n is the number of sides on the given polygon and a is the interior angle of each vertex, you can find the necessary crimp angle for any star polygon. The 75-degree angle lets the units have a slightly wider dihedral angle than perfectly angled crimps would allow.

    Book and cupboard fold; unfold.

  • How to fold an origami shape. The Alphabet - Step 15
    Step 15

    Pivoting along the center crease, join the circled areas, folding where shown.

  • How to fold an origami shape. The Alphabet - Step 16
    Step 16

    Swivel-squash fold along existing creases, folding the left quarter in.

  • How to fold an origami shape. The Alphabet - Step 17
    Step 17

    The result. Rotate 180 degrees.

  • How to fold an origami shape. The Alphabet - Step 18
    Step 18

    Repeat Steps 2–3 on the other side of the paper.

  • How to fold an origami shape. The Alphabet - Step 19
    Step 19

    Tuck the locks under the top layer.

  • How to fold an origami shape. The Alphabet - Step 20
    Step 20

    Join the circled edges, and unfold.

  • How to fold an origami shape. The Alphabet - Step 21
    Step 21

    Fold the unit in half horizontally; unfold.

  • How to fold an origami shape. The Alphabet - Step 22
    Step 22

    Join the circled edges and unfold.

  • How to fold an origami shape. The Alphabet - Step 23
    Step 23

    Fold up where shown, along the bottom of the crease made in the previous step; unfold.

  • How to fold an origami shape. The Alphabet - Step 24
    Step 24

    Fold an angle bisector of the previous two steps.

  • How to fold an origami shape. The Alphabet - Step 25
    Step 25

    Pivoting along the horizontal center crease, join the left edge to the edge of the angle bisector on the right, folding where shown; unfold.

  • How to fold an origami shape. The Alphabet - Step 26
    Step 26

    Fold between the circled areas; unfold.

  • How to fold an origami shape. The Alphabet - Step 27
    Step 27

    Fold in half and unfold. Then flip over.

  • How to fold an origami shape. The Alphabet - Step 28
    Step 28

    Crimp the unit as shown, mountain folding the unit in half vertically.

  • How to fold an origami shape. The Alphabet - Step 29
    Step 29

    The completed unit. Side view.

    Steps 9–11 are used to make a 75-degree crimp angle. If you feel comfortable doing so, you can omit these steps and approximate the fold made in Step 12 to save time.

  • How to fold an origami shape. The Alphabet - Step 30
    Step 30

    Assembly

    Before assembling the units, flatten the dihedral angle around the vertices of the units you are assembling. Then slide the tabs around and into the pockets. Two units will join at every vertex.

  • How to fold an origami shape. The Alphabet - Step 31
    Step 31

    Finally, push in the sides of the units where shown, recreasing the center dihedral angle.

  • How to fold an origami shape. The Alphabet - Step 32
    Step 32

    Two units joined. Join the others in the same fashion.

  • How to fold an origami shape. The Alphabet - Step 33
    Step 33

    One complete icosikaipentagonal star, composed of twenty-five units. The name sounds intimidating, but it is simply the geometric name for a twenty-five sided polygon. It is called a star because it is a stellated polygon rather than a regular one, but is not an icosikaipentagram. Thus this model is composed of twenty-six interlocking twenty-five-sided stars.

  • How to fold an origami shape. The Alphabet - Step 34
    Step 34

    Weaving Instructions

    This model is very different from all others in this book. First, it is critical to recognize that it has polar dihedral symmetry; there will be a large “hole” on the top and bottom of the model. There is no regular polyhedron on which this compound is based; therefore the assembly will rely on axial weaving.

  • How to fold an origami shape. The Alphabet - Step 35
    Step 35

    Basically, there are twenty-five polygonal “bands” that weave around each other to form the large “holes” on either side of the model. The twenty-sixth frame wraps around the center of the model, and is the only frame that has no interaction with the poles. In the photos below, the twenty-sixth frame is the light-blue band that is fully completed, and the pieces of other frames are parts of the center.

  • How to fold an origami shape. The Alphabet - Step 36
    Step 36

    The weaving of this model is actually simpler than you might think, once the pattern is understood. The schematic above shows the center light-blue frame—represented by the light-blue segment—and its equatorial relationship with other frames. There will be ten four-fold axes along each “file” of the model.

  • How to fold an origami shape. The Alphabet - Step 37
    Step 37

    The actual weaving between the frames should be obvious—each vertex where two units join should weave over the “valley” crimp of another unit.

  • How to fold an origami shape. The Alphabet - Step 38
    Step 38

    Along each “file” of the model, starting at the center twenty-sixth frame, there will be one five-fold axis, followed by ten four-fold axes, followed by one three-fold axis near one of the poles, before the frame bends back down into the model as indicated by the arrow on the photo at the top left of the facing page.

  • How to fold an origami shape. The Alphabet - Step 39
    Step 39

    This pattern is repeated along each “file” around the entire model. All frames, with the exception of the twenty-sixth center frame, are hyperboloidal.

  • How to fold an origami shape. The Alphabet - Step 40
    Step 40

    The number of assembled units in each picture is not specified since units can be added randomly, as needed. Also, the nature of the crimped units should make frameholders unnecessary, even in the earlier stages. The below right and top left facing page photos show the first complete pole forming.

  • How to fold an origami shape. The Alphabet - Step 41
    Step 41

    As the model gets closer to completion, its weight and shape will necessitate that it be tipped onto one of its poles (the large open holes with twenty-five-fold axes on opposite sides of the model).

  • How to fold an origami shape. The Alphabet - Step 42
    Step 42

    As the frames approach completion around the equatorial regions, the light-blue twenty-sixth frame might deform a little because the other frames still aren’t in their final positions.

  • How to fold an origami shape. The Alphabet - Step 43
    Step 43

    Push down gently on the poles to help alleviate this problem. Additionally, note that along each “file,” the chirality of every axis is opposite to the ones on either side of it.

  • How to fold an origami shape. The Alphabet - Step 44
    Step 44

    Further, this model has an in-and-out weaving relationship between any two frames, which is helpful if you need to double-check the weaving.

  • How to fold an origami shape. The Alphabet - Step 45
    Step 45

    If you manage to complete it, congratulate yourself; this is the largest and most time-consuming model in this book, which is why I have left it for last.

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amalia.syamra
amalia.syamra · Kampar Kiri, Riau, ID · 12 projects
Look so hardSad
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