Folding instructions:
Starbursts

A photo guide to folding the tessellation, Starbursts. The tessellation primarily uses open hexagon twists and closed triangle twists.

There are two main variants: a flat version and a raised version, which depends on which final finishing step you select.

Variation 1: Flat starbursts.

Variation 2: Raised starbursts (angled view).

This guide uses 35cm blue tant, which has been cut into a hexagon with ~7" sides, and divided into a 48-triangle grid.

Most of the folding will be done on what ends up as the back side (the triangle twist side). In the last step, flip the paper over to do the finishing touches on what ends up as the front side (the hexagon / starbursts side).

Step 1: Initial molecule

This molecule is folded at the center of the paper.

1.1: Open hexagon twist

Start with an open hexagon twist at the center of the paper.

Completed: an open hexagon twist.

1.2: Fold back towards center

Fold each pleat back towards the center, crossing the hexagon. You may need to reopen the first pleat slightly in order to get the last pleat to fold over neatly before flattening the whole setup. This is based on Fujimoto's basic hexagon pinwheel methods.

Diagram showing how to fold each pleat towards the center.

In progress: 3 pleats folded towards the center.

Completed: the pleats radiate out from the center once complete.

On the flip side, you'll find a smaller hexagon that looks as if it were made with a closed hexagon twist, but is actually the center of the open hexagon twist.

1.3: Triangle twists at each corner

On each pleat, count out one triangle from the center and fold a closed triangle twist.

Diagram showing where the triangle twists are placed (half of each twist is hidden by the pleat).

In progress: A single triangle twist.

In progress: 3 triangle twists. Just fold over the edge overlaps for now, they will resolve into new hexagon twists later.

Completed: 6 triangle twists. The final edge overlap doesn't match the other 5, which doesn't matter because we'll be unfolding them in the next step to add the next ring of molecules.

The initial molecule is complete!

Step 2: First ring of repeats

Fold a new ring of molecules surrounding the center one.

2.1: Fold a new open hexagon twist

Temporarily fold back pleats, crossing the triangle twist, of two adjacent triangle twists. This will provide the start of a new open hexagon twist. Continue adding pleats to complete the twist.

In progress: Pleats folded back against two adjacent triangle twists. You can start to see where the open hexagon twist will resolve.

In progress: Add additional pleats to create the rest of the open hexagon twist.

Completed: The flattened hexagon twist.

2.2: Fold back the pleats towards the next hexagon center

Repeat step 1.2 but with the new hexagon twist as your center.

In progress: 3 pleats folded towards the new hexagon's center. The original hexagon's triangle twists have reappeared.

Completed: a set of pleats radiating out from the new hexagon's center, connected to the previous hexagon via triangle twists.

On the flip side, you can now see two adjacent hexagons.

2.3: Complete the ring by adding new hexagons, connecting via triangle twists

Repeat 2.1 and 2.2 to add additional hexagons and complete the ring. It is easier to add a 120° pleat intersection to connect to the previous hexagon in the ring, flatten the new open hexagon twist, and then flatten the triangle twist connection when folding the pleats back into the new hexagon twist's center.

In progress: A new open hexagon twist flattened. It is connected to the previous open hexagon twist via a temporary 120° pleat intersection.

In progress: The pleat intersection is flattened into a triangle twist when folding the pleats back to the center of the new hexagon twist.

In progress: Continue adding hexagons in a ring around the center. This example shows the last hexagon needed for the ring in the middle of twisting.

Completed: a new ring of radiating hexagon pleats surrounds the center.

The first ring is complete!

Step 3: Additional rings of repeats

Continue folding rings of molecules outwards as grid space permits. At this point, new hexagons can either be at the corners of the ring, or within the sides of the ring. The triangle twist connections are slightly different for each, but resolve to the same point.

3.a: New hexagons at corners

A single triangle twist will be present that needs to be temporarily folded back when adding a new hexagon.

The triangle twist is circled in yellow.

3.b: New hexagons within the sides

Two triangle twists will be present that needs to be temporarily folded back when adding a new hexagon.

The triangle twists are circled in yellow.

Step 4: Finishing

There are several options for finishing the tessellation, where the small hexagons on the side opposite the triangle twists are further shaped.

Variant 0: Leave as-is

The tessellation can be left as-is, for a dense hexagon-and-triangle piece that is similar to Shuzo Fujimoto's Galaxy (銀河), although it won't resemble stars if you do so.

The flat hexagon base, if you prefer a dense hexagon view instead.

Variant 1: Flat starbursts

Each hexagon can be raised, twisted, and reflattened. This creates "rays" between each hexagon so that they resemble stars.

After raising a hexagon, rotate it 60° -- that will keep its sides aligned with the grid, but pull the connecting pleats along. Flatten the pleats so the hexagon lies flat again.

Variant 2: Raised starbursts

Each hexagon can be raised, crimped, and left "floating" above the plane of the tessellation to create puffier star shapes.

After raising a hexagon, pinch the corners together in order to crimp the sides. You can also curl the connecting pleats (slightly twisting the hexagon's orientation, up to 60°). This should allow the pleats to stay risen.

Notes

A 48-triangle grid (hexagon base) allows for 3 rings of repeats.
A 64-triangle grid (hexagon base) allows for 4 rings of repeats.
The ratio a/L is 5/7 if you want to fold this on a rotated grid.
A paper that creases and recreases easily and sharply is the best choice for this tessellation.
- For the flat starbursts variation, you will probably want a relatively thin paper, as the hexagon edges are fairly thick with layers, such as kami or biotope.
- For the raised starbursts variation, you may want a thicker paper that will remain standing after you shape the edges, such as tant or kraft.
If you wish to show off the backlit view, choose a thinner/lighter color paper. Both variants have interesting backlighting but it is easier to see with the flat variation.
Try coloring the hexagons for extra texture in the final view.