Hybrid Hex Weave Origami Tessellation

An Unusual Symmetry

These hybrid hexagon twists (there's actually two kinds) are 3-fold rotationally symmetric.

This is weird for something with 6 pleats - usually these kinds of twists have 6-fold rotational symmetry.

But by putting the 3-fold six-pleated twist in the middle, I was able to push the remaining two 3-fold symmetries out to the next hexagons and use two different kinds of triangle twists.

And so Hybrid Hex Weave uses three different kinds of hexagon twist and two different kinds of triangle twist while the simplest patterns in this tiling use only one of each type of twist.

I've found other varieties of patterns that use two hexagons and one triangle, or two hexagons and two triangles, but no other patterns with three hexagons and two triangles (yet).

Tessellation Details

Can you spot which spots have the hybrid hexagon?

They look a lot like closed triangle twists, but in this case the hybrid hexagons have three open triangles around them and the closed tirangles seem to have two open hexagons.

Likewise, each of the hexagon twists (hybrid included) have three closed and three open triangle twists around them.

Another way to spot them is to triangulate between three open hexagons or three closed hexagons - there's always a hybrid hexagon in the middle.

View From All Sides

From the front of this piece, the hybrid hexagon twist looks very much like a closed triangle twist.

From the back, however, it resembles a large triangle twist that mysteriously has two pleats coming out of each corner!

You can spot the hybrid because the edges of the "triangle" on the back are on grid lines, unlike the other triangle twists.

Three of the pleats outline the edges of the triangle, and the other three are tucked underneath.

I don't have a tutorial for this twist yet - expect it by the end of June.

Alignment of Repetitions

In this particular folding of Hybrid Hex Weave, I chose to use a diagonal grid on a hexagon even though that wasn't strictly aligned with the repeats in the pattern.

As you can see, I let the pattern come very close to the edge and I have notches out of my perfect hexagon border.

Next time I'll either leave more space on the edges or actually align with the pattern repeats.

All three of the hexagon twists used are centered on grid intersections, so all three are equally useful as centers of the tessellation.

Which hexagon twist - closed, open, or hybrid - would you put in the center?

Drop a comment below and then grab the crease pattern to fold it yourself!