## 30-60-90-Degree Star (variant B)

A variant of 30-60-90° Star, just like the base variant, folded from triangles left over when cutting hexagons from rectangles.

Abstract modular origami, usually representing highly symmetric geometric shapes, is the most popular kind of modular origami.

This page lists **models** of a single type. You might be interested in folding instructions instead.

A variant of 30-60-90° Star, just like the base variant, folded from triangles left over when cutting hexagons from rectangles.

A regular dodecahedron made from Penultimate Unit, designed by Robert Neale. These units are very simple to fold and very versatile.

A cube made from Penultimate Unit, designed by Robert Neale. These units are very simple to fold and very versatile.

It’s been a while since I last worked on modular stars, but I designed this one, along with a few variants, at the end of 2023. Variant A is rather fragile a...

I folded this cuboctahedron from modified Open Frame Units (Tomoko Fuse) around 2013. Just 12 units are used, and without modification, they would create a r...

Yet another approach to making a cube from two identical units. This design is paper-effective, and looks very clean from the top and the sides. Looking at t...

The complete set of seven Tetris pieces, recreated in origami using the business card cube module. Of the seven pieces, six require the same number of units ...

I think this is the last star from my 2019 modular star craze that I haven’t published before.

A spiked icosahedron made from my Weird Asymmetric Sonobe (WASS) unit variant with color change. Since the color change’s symmetry is not aligned with the sy...

Another design from my 2019 modular star phase.

In early 2023, I went back to an idea I had in 2016 to make a modular daisy out of bent modules, all connected in the center of the flower. My first attempt ...

A modular recycling symbol, my design from 2021. Mathematically speaking, it is a Möbius strip. Folded from three units, each forming one corner of the trian...

Each link of this chain is a Möbius strip folded from a single CBU unit, essentially a Möbius Strip V (CBU). For a chain with regular, round links, see Chain...

This is just a single long Conveyor Belt Unit (CBU) wound into a coil, but it looks like the Tower of Babel in Bruegel’s painting or the Guggenheim Museum.

This model is just a friendly reminder that almost any tessellation can be transformed into a BBU tile, and combined with other tiles to create 3D shapes wit...

A simple modular star I designed in 2019. I used paper with a heavy pattern which unfortunately masks the crease lines to such degree that practically only t...

Comparison of three related Sonobe variants of mine, from left to right: Paper Airplane Sonobe, Checkered Sonobe, and Bow-Tie Sonobe. Each icosahedron is fol...

It’s been a while since I posted a modular star design, so here is another, from late 2019 when I was very much into this genre. This one has octagonal symme...

I photographed this model ten years ago, in January 2013. It is just a simple tetrahedron folded from Francis Ow’s 60 degree unit. What makes it more interes...

Since today is Polish Independence Day, I’m publishing a picture of my Hedgehog Star III folded in Polish national colors. This work uses a proper color chan...

A follow-up design to Hedgehog Star II from February. There is a color-change, but in this fold I used two kinds of metallic paper, each same color on both s...

Spiked icosahedron, folded from my Checkered Sonobe units.

Another fold of Hedgehog Star II, once again in Ukrainian national colors since symbolizing Ukraine’s resistance in the face of Russia’s aggression was the r...

A variant of Star Phobos that has additional decoration in the center of the star on the front side.

A modular star I designed in early 2020. There are several ways in which the units can be connected, of which the one shown here is most stable. Since the la...

This is a very simple and elegant traditional model: a ninja star you can actually throw quite well. With just two units it’s also one of the simplest modula...

This is a very simple modular star, this time with square rather than hexagonal symmetry. It looks a bit like a compass rose with only the four cardinal dire...

I designed and folded this spiked origami star bearing Ukrainian national colors last Monday night, after Putin’s speech. The design has a color-change, but...

The 62 Knot is one of three prime knots with crossing number six. Though not as well known as the Trefoil Knot, it is also quite interesting. This origami ve...

This variant of Star Ananke has additional little rays in the center.

You can assemble a simple Christmas tree from multiple Fortune Tellers (which you probably already know how to fold). Each Fortune Teller is smaller than the...

This origami kaleidocycle is an example of a flexible polyhedron, and an action origami model. You can see the cycling action in this video by Ed Holmes, in ...

In contrast to my earlier trefoil knot from CLU unit, which used a more elongated strip of paper and was shaped more like a clover, this trefoil knot is fold...

This Möbius strip is made from a single Conveyor Belt Unit (CBU), just like Möbius Strip V, but the ends are twisted additional 360° before being connected. ...

A variant of Star Eris with modified center.

Yet another simple design from the time I got into modular origami stars. Unpublished version 1.0 used a less effective lock between the units.

A Möbius strip consisting of a single Conveyor Belt Unit (CBU) twisted and locked with itself by both ends. This is the cleanest representation of a Möbius s...

A conveyor belt, made from Conveyor Belt Units (CBU). Instead of connecting the ends together, one could also leave the model in the form of a flat tape, or ...

When I was little, it was common for kids to make paper chains as Christmas tree decoration (łańcuch na choinkę). These chains were made by cutting colored p...

In this variant of Star Deimos, units are modified so that there is no pocket in the top visible layer. This requires a change to the locking mechanism and r...

A trefoil knot from a single Cross Lap Unit.

Another cube from BBU-s: 6 × E7, 6 × D4 6 × A1.

A spiked icosahedron made from Weird Asymmetric Sonobe (WASS) units.

The units from which this star is made, are folded from triangles whose angles are 30°, 60° and 90°. Such triangles are created when you cut a hexagon from a...

A variant of Star Deimos in which the rays are asymmetrically narrowed on one side, giving the star’s outline the appearance of a saw blade.

I designed this model for the cover illustration of my father’s book on nanoparticles. It represents the structure of SBA-15, a type of mesoporous silica. My...

Variant B of Star Deimos differs from the base shape only by a single fold which reveals more of the white side of the paper in the center.

Spiked icosahedron, folded from my Bow-Tie Sonobe units (also independently designed by tomoko07011209 around the same time).

This is a model I designed and folded back in 2016. It is made from the same kind of units as Single-Module Modular Heart. Any number of units can be used si...

This was an experiment with yet another PHiZZ variation of mine, conducted a few years ago. I chose too soft paper (or too large sheets) for this model which...

Another simple model in which a cube is built from just two units. See also: Two-Unit Cube I.

Spiked Icosahedron made from my new Sonobe variant, Paper Airplane Sonobe. When you look at an individual unit before assembling the model, you can spot a re...

This is a very simple modular origami design I recently came up with when revisiting my Oxi unit from a few years ago. The unit has folded edges on one side ...

Variant B of my Star Chaos. Modular origami model from 6 units. Duo paper courtesy of a friend.

Star Deimos, another of my simple modular origami star designs. There is a color change in the center of the model, and the six-fold symmetry allows for seve...

An octagonal modular star. Own design, folded from Harmony paper.

Yet another variant of Star Ananke. Variants of this design were designed independently by myself and by others before me: Wei Fu, and Robin Glynn (with mino...

This variant of Star Ananke features an additional hexagon in the center of the model. It’s a small change in the individual unit, but it makes connecting th...

This is the front of Star Ananke, variant D. The basic variant (A) was designed independently by myself and by others before me: Wei Fu, and Robin Glynn (wit...

This is the back side of Star Ananke (variant D). The basic variant (A) was designed independently by myself and by others before me: Wei Fu, and Robin Glynn...

A modification (variant C) of Star Ananke. The basic variant (A) was designed independently by myself and by others before me: Wei Fu, and Robin Glynn (with ...

I prepared this composition as decoration for the room where I would be holding origami workshops related to my exhibition at Olsztyn Planetarium. During the...

Modular origami stars are quite addictive: I set out to create just one simple model for a workshop and before I knew it, I had about a dozen different desig...

A modification (variant B) of Star Ananke. The basic variant (A) was designed independently by myself and by others before me: Wei Fu, and Robin Glynn (with ...

As part of preparations for my presentation and workshop on contemporary origami, I set out to design a simple modular star which I could teach in the worksh...

A Greek meander pattern folded as modular origami. The bent frame technique is the “Thoki Yenn style” which I also employed in a number of other models, for ...

Shuzo Fujimoto’s Hydrangea can be used as a modular unit. The method was first published by Meenakshi Mukerji and then reinvented independently by myself. I ...

A modified version of Lelum Polelum Cube where one out of each pair of flaps is hidden.

A Cube from a unit I recently designed and later learned that was earlier designed independently by Saburo Kase. More details in the unit’s description.

Another fold of Five Intersecting Tetrahedra (FIT), this time with silver metallic paper.

This is the logo of Apache Mesos (cluster management software) rendered in origami. A colleague at work suggested I try designing this object in origami afte...

Aton Kusudama, variant A (many more are possible). Spiked icosahedron made from 30 units. Designed and folded by me. More variants are possible, some with in...

This is a real-life rendition of the TensorFlow logo in origami, using the Business Card Cube Unit.

90-edge buckyball made from a variation of Tom Hull’s PHiZZ unit. I know that other people have also designed this simple variant of the unit independently f...

This kusudama is a refold of an old spiked icosahedron model of mine with nicer paper. It’s a modular design which uses 30 units.

The Möbius band (aka Möbius strip) is an interesting mathematical object, a single-sided surface. This origami version is folded using my Cross Lap Unit (CLU...

Origami heart made from a single Cross Lap Unit (CLU), using a similar technique as my Ichthys. Metallic paper with acrylic paint.

Easter is coming so with fluffy bunnies and cute chickens aplenty, it’s good to also add this fish to the pack.

Lotus Cube, made from a variant of my BBU (Building Block Units). Even though it is possible to make a cube from just 6 lotus BBU units, such an assembly is ...

This modular woven polyhedron not only looks nice, but it also has a very interesting history of different people designing it independently. Those credited ...

This heart is made from a single module which is a modification of 90-degree unit (independently discovered by me and others), so it’s like a modular design ...

This cube is made from a slightly modified variant of my Woven Slit Module (WSM). 36 units are used (6×4 = 24 for the faces and 12 for the edges), made from ...

This is an icosahedron (or dodecahedron, depending on how you look at it) made from a modified version of Sturdy Edge Module (StEM), a 90-degree unit variant...

This cube is made from six units, each of which is a recursive four-sink base modified for use as a module.

This is an example of using my Fractal Pinwheel as a modular unit. Due to small size, there’s only one level so the fractalness is not so clearly visible.

This rendition of the Tower of Babel consists of a series of square platforms placed one on top of another and rotated by 45 degrees at each level. This frac...

Spiked octahedron made from my Woven Slit Module (WSM), 48 units from 3:1 paper.

Made from my Building Block Units (BBU), modified E9 variant.

After I made a Hydrangea Cube, Hydrangea Icosahedron was the next logical step. Just as in the cube, the Hydrangea Tessellation by Shuzo Fujimoto is used as ...

This is about as simple a model as it gets (just 6 units).

In this assembly method, units forming each face of the cube are woven, forming a hole in the middle. This increases the number of units needed for a cube to...

In this assembly method, units forming each face of the cube are woven, forming a hole in the middle. This increases the number of units needed for a cube to...

In this assembly method, each of the cube’s faces is made of two modules which are both attached to both perpendicular modules in the same way. Together with...

This cube is a mechanical toy. Its size can be adjusted: the cube can grow or shrink by a factor of about two. It starts out as a cube with a pattern resembl...

Another combination of Building Block Units and tessellations, this time Fujimoto’s Clover Folding, folded without the decorative margin. 18 modules: 6 × BB...

This is a modular cube made of six Square Weave Tessellations. The connection method is mine, the authorship of the Square Weave Tessellation seems to be dis...

I came up with the idea of connecting Hydrangeas to form a modular origami design independently, then found out Meenakshi Mukerji had published it in her boo...

This model is a combination of Building Block Units and Fujimoto’s Clover Folding. The models amounts to 18 units, 12 of which are BBUs (6 × D10 variant, 6 ×...

Named after a poem, this model is — strictly speaking — just a spiked icosahedron.

A single-sided surface, the Möbius Band is one of the more interesting mathematical objects that can be reproduced in origami.

Makalu is one of the models in Robert Lang’s Himalayan Peaks series. Its more scientific name is six intersecting pentagons, or: 6 × 5 × 1 polypolyhedron. Se...

This is the simplest of Robert J. Lang’s polypolyhedra. A more descriptive name of this model is four intersecting triangles, or 4 × 3 × 1 polypolyhedron.

Annapurna (also known as ten intersecting triangles or 10 × 3 × 1 polypolyhedron) was designed by Robert Lang, but the model presented here uses my Sturdy Ed...

The structure of this model is similar to spiked icosahedra made with variants of the Sonobe unit and other similar modules. However, in the case of BBU, a t...

This model consists of flat bands of units which create an outline of the rhombicuboctahedron. It uses 48 modules: 18 × D4, 18 × A2, 12 × A4.

This model demonstrates how Building Block Units can be modified to form rectangular rather than square faces. Just like the cube, this model uses 12 modules...

Model uses 192 modules: 120 × A1, 72 × A2

This structure can be extended indefinitely to fill the plane with a hexagonal pattern. By adding more layers it can also be expanded up and down.

A Hamiltonian cycle is a closed path on a polyhedron which visits each vertex exactly once. This model represents such a path for a cube. It can also be used...

This is a shape created by placing cubes on the outer square walls of a hexagonal prism. This way, the outer outline becomes a dodecagonal prism. Seen from t...

Due to the E10 tile’s small flaps, it can’t be directly attached to the flaps of inner A1 tiles. An additional “sizing” layer of A2 tiles is needed for prope...

Cube from 12 modules: 6 × D9, 6 × A1.

Cube from 12 modules: 6 × D18, 6 × A1.

This composition is made from 75 modules: 36 × A1, 30 × A2, 6 × D1, 3 × E4.

Compare with the same solid folded from standard Sonobe units.

Compare with an octahedron built using the same technique (octahedron’s page also discusses the technique in more detail).

Mathematically speaking, this wheel is a tetradecagonal prism. This construction, which uses a mix of units made from 1:√2 and 1:2√2 paper, isn’t mathematica...

This cube uses PVM Edge Connector Units to create extra distance between the Vertex Modules.

The result of using the sunken variant of PVM Vertex Unit is a cube with four vertices replaced by inverted pyramids.

This is a physically large model which demonstrates how StEM units made from sheets of different proportions can be combined (obviously, all rectangles’ shor...

Normally, Toshie’s jewel is made from Sonobe units, but this one is made from StEM units instead.

In this model, each face of an icosahedron was replaced with a triangular pyramid made from three units.

The unit is a variant of an edge unit; I call usage like this the “face variant” since the unit covers a face rather than an edge of the solid. When I invent...

This model’s structure is an octahedron whose each face was replaced with a pyramid of three equilateral right triangles, pointing inwards. Units are located...

The modules’ shape makes this level 1 model look even closer to a level 2 model than the Penultimate Module version. The hole in each small square is exactly...

This model shows how StEM units can be modified so that their short rather than their long axis is aligned along the model’s edge.

This model (first from the left) is compared here with some other simple polyhedra folded from the same kind of module. Note how the tetrahedron looks almost...

This model (first in bottom row) is shown compared to other models folded from SEU units made from 2:1 and square paper (top and bottom row, respectively). N...

This model (first in top row) is shown compared to other models folded from SEU units made from 2:1 and square paper (top and bottom row, respectively). Note...

This model demonstrates the rotated link connection method that can be applied to SEU units folded from square paper, which can be considered a Sonobe varian...

This model demonstrates the Sonobe link connection method that can be applied to SEU units folded from square paper, which can be considered a Sonobe variant...

This model demonstrates the reversed SEU link connection method that can be applied to SEU units folded from square paper, which can be considered a Sonobe v...

This model demonstrates the SEU link connection method that can be applied to SEU units folded from square paper, which can be considered a Sonobe variant. T...

This ring can also be worn as a headband. It uses a non-standard way of connecting the modules. Any even number of modules can be connected this way, though ...

Compare this model with a version folded from SEU units.

Compare this model with a version folded from StEM units.

This model (first from the right, top row) is compared here with some other simple polyhedra folded from the same kind of module. The two octahedra demonstra...

This model (first from the right, bottom row) is compared here with some other simple polyhedra folded from the same kind of module. The two octahedra demons...

This model (last in bottom row) is shown compared to other models folded from SEU units made from 2:1 and square paper (top and bottom row, respectively). No...

This model (last in top row) is shown compared to other models folded from SEU units made from 2:1 and square paper (top and bottom row, respectively). Note ...

This model (second from the left) is compared here with some other simple polyhedra folded from the same kind of module.

This model (second in bottom row) is shown compared to other models folded from SEU units made from 2:1 and square paper (top and bottom row, respectively).

This model (second in top row) is shown compared to other models folded from SEU units made from 2:1 and square paper (top and bottom row, respectively).

Made from Tomoko Fuse’s Open Frame II (plain) unit, polyhedron design by me.

See also the same design with different coloring.

Made from Tomoko Fuse’s Open Frame I (bow-tie motif) unit, polyhedron design by me.

This is a labor-intensive, but very satisfying to fold model. Some people have managed to go as far as level 3 but even level 2 was quite challenging. About ...

Another fold of the Compound of Five Tetrahedra, with different colors. I used this model to make anaglyph images which allow you to see it in 3D (with red-c...

Model folded from a unit I made specially for this purpose.

I designed the simple unit used for this model and later learned that it had been already published before by Jose Arley Moreno.

Model folded from Warsaw public transport tickets (back side with magnetic strip visible). 192 modules: 120 for the body and 72 for coating.

I folded this business card cube from Warsaw public transport tickets rather than from business cards. 12 modules: 6 for the body and 6 for the coating.

This was one of my early modifications of the 60° unit. Note that in this modification, the angle at the module’s tip is NOT 60 degrees.

Compare with a dodecahedron constructed from units modified by me in a similar manner, and with a model with the same structure but using StEM units.

Compare with an icosahedron constructed from units modified by me in a similar manner.

I think this is my first Sonobe variant. Since it’s one of the simplest modifications possible, it has probably been independently discovered by many others.

You can compare this model, which uses straight, unmodified units, with two models made from the same units after slight modification: Flower Icosahedron and...

The module, originally designed just for folding this dodecahedron, can be also used for other kinds of models. See, for example, this spiked icosahedron.

Model is placed near a real Poinsettia flower for comparison.

Just like the pyramid, this is a shell with an empty inside.

The model’s name is a reference to the Golden Sphere from Roadside Picnic.

This model is made from 90 modules (modified variant for triangular faces). Each face of the dodecahedron is made from a 5-triangle group, where the triangul...

At only 30 modules, this model is still much more challenging than most models with several times that many units, but also a lot of fun to fold. See the lin...

Generally, PHiZZ units are always connected in such way that three modules meet at each vertex. However, one can connect just two modules at some points, thu...

This is my experiment in modular origami made from two different types of units: 60 PHiZZ and 60 Penultimate units. These two kinds of modules are quite simi...

You can squeeze this model and transform it into an icosahedron, closing the empty space between units. This is called the jitterbug transformation.

A small modification used in this model makes it possible to create polyhedra with triangular faces from Penultimate unit in a more convenient way than origi...

One of the larger models I have designed, this icosidodecahedron has pentagonal faces made up of small triangular pyramids and triangular faces replaced with...

See also: icosahedron from same units but pointed inwards.

See also: icosahedron from same units but pointed outwards.

This model was quite difficult to design, as the two sides of surfaces made with PHiZZ modules differ a lot (due to the presence of “bumps” where units join)...

There is one spike placed over two adjacent faces of the pentakisdodecahedron in this model. I haven’t checked if the angles actually add up, so it might be ...

Model is also known as WXYZ Diamonds.

This puzzle, described in Hugo Steinhaus’ book Kalejdoskop matematyczny (Mathematical Snapshots, literally Mathematical Kaleidoscope) consists of six pieces,...

Apart from this basic version, I also made a variant of this model which has additional “fins” on the icosahedron’s edges.

One way of looking at this model is to see it as an icosahedron with a pyramid placed on each triangular face. Another is seeing it as a dodecahedron where e...

This model is similar to the spiked icosahedron, but apart from the spikes on all faces, the icosahedron also has “fins” placed on its edges.

See also the same design with different coloring.

This model uses 128 Trimodules, forming 64 2-unit tetrahedra, and 126 links that connect them, for a total of 254 units. The links were made from narrow rec...

This is one of the rather few modular origami designs which use an odd number of units. Compare also with another similar model.

This is one of the rather few modular origami designs which require an odd number of modules. Compare also with another similar model.

Thanks to the modules’ shape and the holes created in the spaces between them, this model looks almost like a level 2 Menger sponge even though it is actuall...

This icosahedron has nine triangular pyramids pointing inwards on each face. The same shape can also be described as a truncated icosahedron whose each face ...

Compare also with level-1 version of the same fractal.

A level-1 Koch snowflake is just a simple hexagonal star, and this is the way of connecting the Trimodule units originally suggested in Nick Robinson’s instr...

This fractal is an analogue of the standard Koch snowflake. Level 0 is a tetrahedron. In each iteration, a tetrahedron with half the edge length is placed in...

There are six intersecting planar surfaces, each in the shape of pentagonal star, in this model. This leads to the most popular coloring with six different c...