Embedded Files
Tessellations
These tessellations were folded in 2024.
Five by Five
Five by Five
Date: 12/26/2024
Paper: 12" white mulberry paper with white fibers (48-square grid)
From: Origami Tessellations: Awe-Inspiring Geometric Designs
By: Eric Gjerde
Model: Five-and-Four
An extended version of the Five-and-Four model with a denser grid. The thin mulberry paper allows a beautiful backlit pattern.
The back side of the model shows the weaving, alternating between squares and rectangles.
Backlit, the edges of the squares are dark, with lighter connections between squares.
Backlit, the backside shows a softer contrast between the weaves, and also shows off the fibers in the paper.
Hex and Triangle tests
Hex and Triangle tests
Date: 12/xx/2024
Paper: 12" diameter hexagons, orange mulberry paper / purple mulberry paper (32-triangle grid)
Some tests using mulberry paper for tesselations. While thin and soft, it allows for light to shine through and highlights the interesting patterns created by overlaps. One model uses both open hexagon and triangle twists while the other uses closed hexagon and triangle twists (with pinwheeling of the hexagons) and although very similar in shape arrangement, the size of the molecules really stand out as different.
The open hexagon/triangle combination is also known as Celtic Circle by Robin Scholz.
The backlit open hexagon and triangle twist model.
The closed hexagon and triangle twist model is much denser.
Backlit, the closed hexagon and triangle model has sharper contrast between single- and multi-layered areas.
Lacy Snowflake
Lacy Snowflake
Date: 12/18/2024
From: Origami Tesselé
By: Lydia Diard
Model: Pavage #389
Paper: Hexagon cut from 35cm diameter hexagon, light blue tant (64-triangle grid)
While the base pattern is the same as Eric Gjerde's Spread Hexagon model, this one connects the edges together instead of letting them ripple outwards, leading to a very different feeling. The original model uses sharp creases at the center of the hexagon, but the small size of the final grid made that difficult so I opted for rounded corners, which give it a lacy, floral feel.
The back side of the model shows a simple hexagon stacking.
Backlit, the edges that connect each hexagon show up more clearly, along with stars in the center of each hexagon.
Backlit, the backside shows the difference between hexagons that have the stars compared to the hexagons which are just space between them.
Stepping stones
Stepping stones
Date: 12/09/2024
Paper: 8.5" grey Lokta paper with silver highlighting (32-square grid)
An exploration of open and closed square twists, the alternation between large and small squares reminds me of a path paved with stepping stones.
The back side shows a woven pattern.
The difference between closed and open square twists can be seen more clearly when the model is backlit.
Snowflakes
Snowflakes
Date: 12/8/2024
From: Origami Tessellations: Awe-Inspiring Geometric Designs
By: Eric Gjerde
Model: Star Twist
Paper: ~15cm diameter hexagons, radial floral patterned origami paper (16-triangle grid)
Star Twist was the base for a mixture of snowflakes, being a flexible six-sided pattern. By varying the center (hexagon, small hexagon, triangle, pinwheel) and the spokes (broad, narrow, narrow with skirt, short with skirt), I could create 16 unique variants. 32 could be done if I had switched the chirality.
8 snowflakes demonstrating the various center and spoke patterns.
8 snowflakes demonstrating the various center and spoke patterns.
Marbled Galaxies
Marbled Galaxies
Date: 12/6/2024
From: 創造する折り紙遊びへの招待 (Invitation to Creative Playing with Origami)
By: Shuzo Fujimoto
Model: 銀河 (Galaxy - CWF#67)
Paper: 12" mulberry paper with grey/blue/purple marbling (48-triangle grid)
A new exploration of the galaxy pattern, this time with every hexagon turned into a pinwheel.
The model before folding all the hexagons into pinwheels.
Backlit shows the pinwheel patterns more clearly.
Backlit, showing the back side, the connectors between pinwheels is much more apparent.
Colorful Daisies
Colorful Daisies
Date: 12/02/2024
From: Origami Tessellations: Awe-Inspiring Geometric Designs
By: Eric Gjerde
Model: Daisy Chains
Paper: 12" mulberry paper with pink/green/orange/gold marbling (48-triangle grid)
A revisit of the Daisy Chain pattern using the soft, marbled mulberry paper to provide some extra texture.
Marble tile church floor
Marble tile church floor
Date: 11/24/2024
From: Origami Tessellations: Awe-Inspiring Geometric Designs
By: Christiane Bettens
Model: Roman Church Floor Tiling
Paper: 12" mulberry paper with purple/teal/apricot marbling (48-triangle grid)
A revisit of the Roman Church Floor Tiling pattern. Marbled paper provides a much more interesting pattern on the paper, and the denser grid allows exploration of additional hex twists around the center.
The base paper with the grid partially creased, showing the interplay of colors that eventually get woven into the final piece.
When backlit, the difference between zones with central hex twists and the zones without them become more apparent.
Basket Weave (reprise)
Basket Weave (reprise)
Date: 11/xx/2024
From: Origami Tessellations: Awe-Inspiring Geometric Designs
By: Joel Cooper
Model: Basket Weave
Paper: 12" light brown elephant hide; 12" mulberry paper with black/gold/silver marbling (48-triangle grid)
With much more knowledge and experience folding tesselations, I thought it would be fun to revisit the basket weave pattern. The elephant hide paper provided strong creases and it was much easier to get crisp edges and a tight pattern. Meanwhile, the mulberry paper provided a beautiful swirled pattern.
The back side of the elephant hide model, showing the tangle of hexagon and triangle twists.
The marbled paper model, with the edges tucked away to create a full hexagon.
The marbled paper model backlit, showing the weaves and the hexagons between them clearly.
Triforcean Triangles
Triforcean Triangles
Date: 10/09/2024
Original
Paper: 24cm yellow origami paper (32-triangle grid)
The first original flat tesselation I designed, rather by accident. Having started playing Zelda: Echoes of Wisdom, I was thinking about triangles and triforces, and started folding together triangles with 3 pleats per edge, using just 60-degree pleat intersections at each corner. This means there are no twists in this tesselation! This also lead to a neat back side pattern of hexagons.
Changing the overlap of the intersections on the back side could potentially create other backlit patterns, but I chose the simplest, a uniform overlap at each, which creates an alternating triangle pattern in the backlit view.
The back side of the pattern, showing hexagons created by the crossings of all the pleat intersections.
Backlit, the "up" triangles show up darker than the "down" triangles due to the way the overlaps are arranged. The hexagons are faintly visible.
Backlit, the backside hexagons are connected by triangles, which outline a hexagon null space.
Sharkskin
Sharkskin
Date: 10/03/2024
From: 創造する折り紙遊びへの招待 (Invitation to Creative Playing with Origami)
By: Shuzo Fujimoto
Model: カゴメ (Kagome/Lattice - CWF#68)
Paper: 12" dark grey elephant hide (32-triangle grid)
This triangle-only twist design produces a pattern that is the same on both sides of the paper! The dark grey of the paper and the dense triangular texture made me think of the qualities of shark skin.
Halfway through the final collapse step, showing the fully collapsed lines at the top and the partially folded lines at the bottom in a sort of gradient.
Backlit, the space between triangles appears as hexagons.
A close-up angled shot, showing the raised and sunken triangle pattern more closely.
Growth
Growth
Date: 08/28/2024 - 8/30/2024
From: Origami Tessellations for Everyone
By: Ilan Garibi
Models: Childhood, Childhood Evolved, Adulthood
Paper: 15cm pastel origami paper; 24cm teal origami paper; 8.5" lokta paper (various patterns)
Some studies of the Hood family, culminating in several explorations of a single molecule of Adulthood.
2x2 studies of Childhood (left) with 4 triangles per molecule, and Childhood Evolved (right) with 8 triangles per molecule.
A larger 2x2 Childhood Evolved with ivory lokta paper with a blue and black floral print.
The back side of the larger 2x2 Childhood Evolved model, showing the cube and triangle arrangement more clearly.
A single Adulthood molecule in 24cm origami paper. The triangle folds show up sharply.
Adulthood in 8.5" dark purple lokta paper with a silver floral print. The triangles are the softest in this model as this was the thickest paper used.
The backside of the grey lokta paper Adulthood molecule, showing the cube in the center of all of the triangles.
Bagan
Bagan
Date: 08/30/2024
From: Origami Tessellations for Everyone
By: Ilan Garibi
Model: Bagan
Paper: 15cm pink origami paper; 8.5" blue and gold lokta paper
A 2x2 study of Bagan led to a larger 4x4 model in Lokta paper. To show off the marbled pattern of the Lokta print, that model didn't collapse the second tier of boxes.
A 2x2 study of the pattern to learn the basics as well as the tiling.
The 4x4 model, at the first layer of boxes.
An angled view of the model, showing off its 2 layers of folds.
Cube collection
Cube collection
Date: 08/27/2024
From: Origami Tessellations for Everyone
By: Ilan Garibi
Models: Waves, Quadilic, Big and Small Cubes
Paper: 15cm pastel origami paper; 8.5" blue and gold lokta paper
Some 2x2 studies of cube-based tessellations, leading to a 4x4 quadilic in lokta paper. The softer texture and shiny floral pattern really brings out the dimensionality.
The back side of the 4x4 quadilic shows the cube at the center of each molecule more clearly.
From left to right, waves, big and small cubes, and quadilic models.
The back side of each model shows their cube arrangements, which vary in height and placement.
Galaxies
Galaxies
Date: 08/25/2024
From: 創造する折り紙遊びへの招待 (Invitation to Creative Playing with Origami)
By: Shuzo Fujimoto
Model: 銀河 (Galaxy - CWF#67)
Paper: 35cm light blue tant (64-triangle grid)
A larger expansion of the pinwheel collection, which is especially intriguing when backlit.
The backlit model, the pinwheel galaxies surrounding basic hexagons is more apparent.
The back side of the model (full of triangles) when backlit provides an entirely different pattern.
Pinwheel collection
Pinwheel collection
Date: 08/21/2024
From: 創造する折り紙遊びへの招待 (Invitation to Creative Playing with Origami)
By: Shuzo Fujimoto
Model: 銀河 (Galaxy - CWF#67)
Paper: 15cm biotope (red - 16 triangle grid, brown - 24 triangle grid), 24cm dark purple origami paper (32 triangle grid)
I found that Shuzo Fujimoto's 5 self-published books are in the public domain so immediately downloaded and studied them. Of interest was this crease pattern that looked similar to the 3.6.3.6 design of hexagons and triangles, but with the shapes on opposite sides of the paper! I also found some notes on creating pinwheel shapes from tesselated hex twists, which I also employed in varying patterns on the final projects.
A 16-triangle grid led to a central pinwheeled hex with not quite enough space for surrounding hexes; a 24-triangle grid allowed for a central hex surrounded by pinwheels, and even a couple extra hexes at the corners.
The undersides of each grid shows the arrangement of triangles in a sort of spiral pattern around where the hex is.
The underside of the 24-triangle grid pattern. Here you can see there are 'rows' and 'columns' of triangles oriented in the same direction.
The model is especially beautiful when backlit. The pinwheel hexes create a different light pattern compared to the plain hexes.
Propellers
Propellers
Date: 08/18/2024
From: Origami Tessellations: Awe-Inspiring Geometric Designs
By: Eric Gjerde
Model: Propellerheads
Paper: 24cm light blue origami paper (32-square grid)
By not completely flattening the center twist of each grouping, a pleasing curved shape and dimensionality is produced.
Overhead view, showing that each grouping is offset from the ones next to it, creating an angled slope to the repetition.
The back side of the model, showing the square basis of each grouping set at an angle.
The model before partially flattening the centers of each grouping.
Midnight Sky
Midnight Sky
Date: 07/27/2024
From: Origami Tessellations: Awe-Inspiring Geometric Designs
By: Ralf Konrad
Model: Star Puff
Paper: 35cm dark blue tant (64-triangle grid)
An even denser grid of star puffs! I have been growing fonder of tant paper for tesselations for its sturdier weight and texture, and wanted to try out larger sheets when I discovered this 35cm pack. It allowed me to build up to a 64-triangle grid for the densest star field yet! Sadly, the dark blue I chose was too dark for the LED lights I wanted to use as a backlighting technique, so that will have to be applied to a different tesselation...
Stage 1 of the tesselation process: a full grid of spread hexagons.
Step 2 of the tesselation process: converting to a full grid of triangle twists.
An attempt at using a string of LED fairy lights to backlight the piece did not work as well as I would have liked...
Hydrangea Quilt
Hydrangea Quilt
Date: 07/02/2024
By: Shuzo Fujimoto
Model: Hydrangea
Paper: Illuminated Wave origami paper (16 in various colors)
The gradients of this paper pack were meant for other floral patterns like iris or dahlia, but I knew it would also work well for hydrangeas. It provides different colors for each level of the tesselation, including great contrast in dark (the innermost and outermost layers) and light (the 2 middle layers). Once I had folded almost the whole pack, I started seeing how they could be arranged, and found a very pleasing tile format where the corners could be tucked underneath each other to create an almost postage stamp feel.
A sample of the paper pattern and a folded hydrangea next to it. This one was only 3 layers so the dark core wasn't revealed, leading to my decision to make the final hydrangeas 4 layers deep.
Comparison of the 4-layer version to the 3-layer version shows how much more interesting the dark core layer makes the flower.
Hydrangea collection
Hydrangea collection
Date: 05/xx/2024
By: Shuzo Fujimoto
Model: Hydrangea
Paper: 7cm pink origami paper; 15cm pink origami paper; 11" copy paper
After learning the basics of the hydrangea tessellation from some tutorials on Youtube, I started trying it out in papers of different sizes, from very large paper (allowing for many layers in one piece) to medium paper (with multiple florets in one piece) to a small paper (it just looks cute.)
Superstar Puff
Superstar Puff
Date: 05/04/2024
From: Origami Tessellations: Awe-Inspiring Geometric Designs
By: Ralf Konrad
Model: Star Puff
Paper: 11" copy paper (48-triangle grid)
I just wanted to see how many stars you could get in a dense grid.
Stage 1 of the tesselation process: a full grid of spread hexagons.
Step 2 of the tesselation process: converting the hex corners intro triangle twists.
Comparing a 32-grid and a 48-grid star puff setup shows just how dense the star grid ends up being.
Pink Daisies
Pink Daisies
Date: 05/24/2024
From: Origami Tessellations: Awe-Inspiring Geometric Designs
By: Eric Gjerde
Model: Daisy Chains
Paper: 24cm pink origami paper (48-triangle grid)
After practicing how to fold 48-triangle grids, the daisy chain was the first tesselation folded as the 32-triangle version didn't quite have enough density to get a full ring of flowers around the center.
The underside of the models shows several rings of hexagons surrounding the sunken stars.
Backlit, the pattern shows the mix of hexagons and floral petals, with radiating lines at the edges where the pattern would repeat.
Backlit, the underside of the model shows the sunken stars in place of the flower petals. The hexagons are also more sharply defined.
Bronze Flower Garden
Bronze Flower Garden
Date: 04/28/2024
From: Origami Tessellations: Awe-Inspiring Geometric Designs
By: Eric Gjerde
Model: Daisy Chains
Paper: 12" copper metallic decorative paper (32-triangle grid)
The copper coating of this paper provides a warm sheen on this floral design. The work was framed and given as a gift.
The underside of the models shows a mix of spread hexagons surrounding sunken diamond stars.
Backlit, the pattern shows the mix of hexagons and floral petals.
The framed work, the mat conveniently hiding the left and right edges where a bit of the underside of the paper was showing.
Roman Church Floor Tiling
Roman Church Floor Tiling
Date: 04/22/2024
From: Origami Tessellations: Awe-Inspiring Geometric Designs
By: Christiane Bettens
Model: Roman Church Floor Tiling
Paper: 24cm orange origami paper (32-triangle grid)
A different variation on the hexagon-and-triangle patterns -- only one hexagon is folded into the center of this pattern, although the many triangles are arranged in hexagon orientations.
The underside of the model shows more explicitly how the triangles are arranged in a hexagon layout, with triangles from the hexagon twist appearing in the center.
Backlit, the center hexagon has radial arms reaching out to the start of the triangles, and you can see their arrangement on hexagonal lines.
Red and Gold squares
Red and Gold squares
Date: 04/21/2024
From: Origami Tessellations: Awe-Inspiring Geometric Designs
By: Eric Gjerde
Model: Five-and-Four
Paper: 8.5" red and gold Lokta paper (32 square grid)
The abstract gold pattern on the red paper gets broken up by the square grid, providing some extra texture to this work. It was framed and given as a gift.
Basket Weave
Basket Weave
Date: 04/19/2024
From: Origami Tessellations: Awe-Inspiring Geometric Designs
By: Joel Cooper
Model: Basket Weave
Paper: 24cm pink origami paper (32-triangle grid)
Another mixture of hexagons and triangles, this design compresses them so closely that it creates an illusion of thin woven strips between each hexagon.
The underside of the models shows how tightly the shapes are packed together - the hexagons are basically touching, with the triangles overlapping them.
Backlit, the pattern shows how much paper is in the arms of the weave and how little is in the center of each hexagon.
Backlit, the underside shows the messier mixture of hexagons and triangles.
Star Puffs
Star Puffs
Date: 04/17/2024
From: Origami Tessellations: Awe-Inspiring Geometric Designs
By: Ralf Konrad
Model: Star Puff
Paper: 24cm orange origami paper (32-triangle grid)
A fuller version of the star puff tesselation using a more dense grid, which allows for more stars to be expanded from the paper.
The underside of the model shows where each star is expanded from.
The hexagon holes where the stars are expaned from can be more clearly seen when backlit.
Rhombus Weave
Rhombus Weave
Date: 04/15/2024
From: Origami Tessellations: Awe-Inspiring Geometric Designs
By: Eric Gjerde
Model: Rhombus Weave
Paper: 24cm green origami paper (32-triangle grid)
This uses a diamond pattern repeated across the paper. The diamonds alternate orientation between north-south and east-west. The paper shape in the end also turns into a diamond!
The underside shows an angled cross weave pattern.
Backlit, the lines connecting the diamonds can be seen weaving across the paper.
Open-back Hexagon Twist
Open-back Hexagon Twist
Date: 04/09/2024
From: Origami Tessellations: Awe-Inspiring Geometric Designs
By: Eric Gjerde
Model: Open-back hexagon twist
Paper: 24cm green origami paper (32-triangle grid)
Another take on the hexagon-and-triangle pattern, this time the hexagons are larger than the triangles, making this the opposite of the pinwheel pattern.
Backlit, the radial arms spreading out from each hexagon become much more apparent.
The underside of the model shows off a regular set of sunken hexagons, with the radial arms forming a weave-like pattern.
Backlit, the underside shows the sunken hexagons much more clearly.
Pinwheel
Pinwheel
Date: 04/07/2024
From: Origami Tessellations: Awe-Inspiring Geometric Designs
By: Eric Gjerde
Model: Pinwheel
Paper: 24cm yellow origami paper (32-triangle grid)
Although similar in ordering to the 3.6.3.6 pattern, the larger triangles provide a stronger radial pattern coming out from each hexagon.
Backlit, the hexagons stand out sharply compared to the larger, airy triangles.
The underside of the model has a neat, 6-sided star pattern with sunken triangles.
Backlit, the underside shows the star pattern in a different way. The hexagons are completely masked by the radial arms.
Tiled Hexagons
Tiled Hexagons
Date: 03/26/2024
From: Origami Tessellations: Awe-Inspiring Geometric Designs
By: Eric Gjerde
Model: Tiled Hexagons
Paper: 24cm black origami paper (32-triangle grid)
Although this is a hexagon tesselation, the most notable feature are the flattened triangles that define the corners of each hexagon.
Backlit, you can better see how the edges of the hexagons overlap each other in order to create the triangles at each corner.
The underside of the model shows that each hexagon is actually 2 triangles across per side, twice the size of the spread hexagon pattern.
Five-and-Four
Five-and-Four
Date: 03/25/2024
From: Origami Tessellations: Awe-Inspiring Geometric Designs
By: Eric Gjerde
Model: Five-and-Four
Paper: 24cm pink origami paper (32-square grid)
This square tesselation appears to have a 3x3 grid of squares floating over a 4x4 grid (the five and four refer to the size of each square, not the arrangement of the grid.)
Backlit, the edges of each square are distinct and emphasize the grid even more.
The underside of the model almost looks like the paper is woven between 2 layers.
Backlit, the underside shows off 4x4 grid more strongly, with the intersections of the 3x3 grid appearing almost as negative space.
Spread Hexagons
Spread Hexagons
Date: 03/17/2024
From: Origami Tessellations: Awe-Inspiring Geometric Designs
By: Eric Gjerde
Model: Spread Hexagons
Paper: 24cm black origami paper (32-triangle grid)
My first attempt building something from a dense, 32-triangle grid. The black paper unfortunately shows the edges a little too well, where some of the black has rubbed off due to me folding/unfolding certain areas multiple times in order to get the pattern to lie flat properly.
Backlit, the model isn't quite regular -- I had trouble keeping track of the cardinality of some of the folds, so they are accidentally swapped in several locations.
The underside of the model shows how dense the hexagons actually are.
Sunny Icon
Sunny Icon
Date: 03/17/2024
From: Origami Tessellations: Awe-Inspiring Geometric Designs
By: Shuzo Fujimoto
Model: 3.6.3.6
Paper: 24cm brown origami paper (16-triangle grid)
The triangles surrounding the central hexagon make this look like a sun icon, or perhaps a clock face.
Backlit, lines radiate outward from the central hexagon, making it even more of a sun icon.
The underside of the model shows diamond patterns making up each arm of the sun.
Backlit, the underside shows off the same pattern as the front size, with the radiating arms.
Square Weave
Square Weave
Date: 03/16/2024
From: Origami Tessellations: Awe-Inspiring Geometric Designs
By: Eric Gjerde
Model: Square Weave
Paper: 24cm pink origami paper (15-square grid)
The collapsing layers of this design make the paper look like it's made of several woven strips. The 15-square grid (technically a 16-square grid with the outermost edge tucked in) produces a neat, symmetrical result.
Backlit, you can sort of make out some of the angled squares.
The underside of the model shows the how the squares are angled more clearly (as well as the 16th tucked in row/column.)
Backlit, the underside shows off the regular lines forming the weave.
Single Star Puff
Single Star Puff
Date: 03/16/2024
From: Origami Tessellations: Awe-Inspiring Geometric Designs
By: Ralf Konrad
Model: Star Puff
Paper: 24cm blue origami paper (16-triangle grid)
This design starts as a series of hexagons. With some extra folds to add depth, you can puff out the model to create stars. With a 16-triangle grid, only a single central star was possible, but it was a good first attempt.
Backlit, the model shows off some of the intricasies of its layering.
The underside of the model shows where it gets puffed out. It's like making your own bubble wrap!
Spiked Roll
Spiked Roll
Date: 03/12/2024
Paper: 24cm grey origami paper
After watching numerous D. Hinklay short videos on Youtube, I was inspired to try my hand at tesselations. This design came from a 16-square grid with crossed diagonals. The pattern was collapsed at random until I found a pattern I liked. The underside looks like a bunch of water bomb bases squished together.
The design collapses into a tiny fraction of its expanded size.
Based on some D. Hinklay designs, holding together some of the edges creates interesting secondary shapes.
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