## Dodecahedron (Penultimate Unit)

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

Copy paper (also known as printer paper) is easily available and inexpensive. I don’t use it much for tessellations or figurative models since its folding properties
and looks are far from perfect, but I do find it very well suited for many kinds of modular origami and for test folds. The most convenient form is note blocks
which contain small pre-cut squares, usually with a side length of 8-9 cm. Be careful, though, as quality differs: some brands use precisely cut squares,
some don’t. Paper quality differs a lot as well. In Poland, what is sold in stationery or office supply stores under the name “origami paper”
(*papier do origami*), is almost always somewhat thinner copy paper rather than the kami paper you might expect.

Ilan Garibi has published a detailed printer paper review which is worth reading, and I wrote down my observations about aging of copy paper.

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.

A classic model by Thoki Yenn, folded by me, probably around 2017. DNA Replication is my variant of this design.

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 way to fold your tea tag, this time producing a design similar to the traditional paper boat. Proportions are different (depending on those of th...

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 got this nice viking-style Java Duke from the organizers of JavaZone. Quick origami sketch on the right. It was great to be here. Thank you!

A one-fold hedgehog, part of my series of tea tag origami models. Design from 2019. Folding the tea tag is a good way of making your cup stand out from others.

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 design by Shuzo Fujimoto is a regular pentagram star. It uses a single cut in addition to folding.

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...

This design is an analog of the traditional paper boat but folded from a hexagon. The 120° angle at the top of the sail results in a more slender boat than t...

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...

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 Whirlwind Box is folded from a full 16×16 grid on copy paper. You can have a look at a fold from Tant paper and without the grid for a comparison of the...

Miura Ori is probably the best known origami corrugation. While the model is named after Koryo Miura who designed a variant which was later used for folding ...

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...

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

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

This is the prototype fold of Parallelograms Tessellation. It’s quite representative of my design technique: a quick doodle on a small grid and a rough sketc...

A simple butterfly, folded from a tea tag. Folding the tea tag is a good way of making your cup stand out from others.

Revisiting my Springy Unit, a design from more than 10 years ago, I realized it would be perfect for folding models of hydrocarbon molecules and aromatic com...

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...

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...

The Pajarita (little bird in Spanish) is one of European traditional origami models, especially popular in Spain and Spanish-speaking countries.

Along with the other Clover Folding model, this is the oldest picture of a tessellation folded by me (taken in June 2015).

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...

An improvised model, folded without any reference points.

A simple house from my Building Block Units, designed for a workshop with architecture students.

A simple, one-sided origami submarine I designed a while ago.

This is an improved version of my origami Cottage, made from Building Block Units.

Traditional origami airplane, a part of my series of tea tag origami models. Folding the tea tag is a good way of making your cup stand out from others.

Folding origami during a break at JavaZone 2019 after an interesting talk about JVM performance tuning by Chris Thalinger.

Here is the first model in my tea tag origami series, a Tea Tag Heart.

A quick study of Lucca cathedral as an origami tessellation on my way to the Italian CDO convention.

A new box, aptly named Her Majesty’s Box, taking shape on the train back from the 50th Anniversary Convention of British Origami Society. Both the convention...

Origami is but pieces of colored paper, easily consumed by the elements and forgotten.

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...

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...

Modular origami rendition of Taipei 101, one of the world’s tallest buildings. I thought reproducing this structure’s characteristic staggered facade in orig...

A Business Card Puppy (Larry Stevens) sitting in front of BBU doghouse (Michał Kosmulski).

Dog house designed by me using several modified variants of Building Block Units. All units (3 for the roof and 13 for the walls and entrance) made from squa...

I like Yara Yagi’s Dachshund very much. I will be teaching this model at this year’s Outdoor Origami Meeting so I thought a nice dog like this deserved a mat...

Yara Yagi’s dog is standing in front of a doghouse designed be me specially to match this model.

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 ...

Coaster made from 4 slightly modified Woven Slit Modules (WSM) folded from square paper. The two sides of the coaster display different patterns. Six coaster...

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

Cat designed by Jose Anibal Voyer. Copy paper painted with acryl.

This is the octagonal version of Pinwheel with Color Change.

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 is a simple name plate on which you can place your name and put it on your desk. You can also use it to place descriptions near your origami models on y...

Name Plate variant which has one of the pyramids pointing outside and the other inside. This allows several elements to be stacked on top of each other, like...

Variant of my Name Plate where both pyramids are pointing outwards. Can be used as candy wrapping or to wrap a gift.

I designed this model as cover art for Surface Charging and Points of Zero Charge, a book by my father, Marek Kosmulski. It is a reference work in electro- a...

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.

This is a practical box made from Building Block Units connected using the hook method. I use this box to store all my Crease Pattern drawings of BBU variant...

Willis Tower (formerly Sears Tower) is an iconic skyscraper located in Chicago. The origami model presented here is made from my Building Block Units (768 × ...

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.

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...

This design can be extended indefinitely by adding more and more levels (a smaller, single-level variant is also possible). The walls are angled at 45 degree...

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

A very simple building without many details. I later improved the design while preserving its simplicity (see Cottage 1.1).

Inspired by traditional Polish wooden churches and the wooden belfry in Paczyna.

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.

This particular model is made from 3 modules, but any number of modules from 2 upwards can be used to create similar models. The only limitation is paper’s t...

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.

A Japanese style short-legged table. Have a look at the notes in description of meshed pyramid for a discussion of the relation between these two models.

This model consists of just a 2-cube thick hull of a pyramid. This makes it possible to create a larger model with fewer modules than in the case of a comple...

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

While it may not be obvious at first, this model has some features which make it strikingly similar to the business card table model. The table’s top is cons...

This model is the size of a real chair. Unfortunately, it can’t support enough weight to be sat in. The surface is not covered in additional, “paneling” unit...

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.

Tux the penguin is a mascot of the Linux operating system. The logo was created by Larry Ewing () using The GIMP.

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...