Möbius Chain (CBU)
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...
Mathematical Objects
Models representing a wide array of simple mathematical objects.
This page lists models of a single type. You might be interested in folding instructions instead.
Tower of Babel (CBU)
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.
Heart, Ladybug, and Mushroom on BBU Cube
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...
Spiked Icosahedra from Three Sonobe Variants
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...
Origami in Shades of Gray
This is a collections of my origami tessellations that I framed and hung near the desk I use for folding. The models, all kept in neutral colors, are as foll...
Tetrahedron (Dark Garden pattern)
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...
Scissors Fractal
This is a recursive version of Shuzo Fujimoto’s Scissors (CFW 87). I wanted to call it Biohazard Fractal since it resembles the biohazard symbol, but later d...
Scissors Fractal (alternating rotation)
This is another fold of Scissors Fractal, a recursive model I derived from Shuzo Fujimoto’s Scissors (CFW 87). In this fold, the direction each level rotates...
Comparison of Scissors Fractal Variants — alternating and consistent rotation direction
A comparison of two variants of Scissors Fractal: one with consistent rotation direction for all levels and one with alternating rotation directions.
Spiked Icosahedron (Checkered Sonobe)
Spiked icosahedron, folded from my Checkered Sonobe units.
Hypar (Hyperbolic Paraboloid) clean fold
The Hypar is usually folded starting from a complete grid, but precreasing it cleanly is rather straightforward. This design is very elegant, so I’m includin...
Fujimoto Cube
This cube, folded from a single square, is one of Shuzo Fujimoto’s most famous designs. Not only is the model very firm, but the folding sequence is a master...
Stacked Whirlwind Molecule
This is a single molecule which can be tessellated. It is made from a molecule of Whirlwind Tessellation placed inside a larger one. More than the two levels...
62 Knot (CBU)
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...
Lucky Star Fractal Box (Simplified) Variant B
When you fold variants of my Lucky Star Box, you can extend the star to its fractal form. This particular variant emerges when you apply that procedure to th...
Fortune Teller Christmas Tree
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...
Dodecagonal Kaleidocycle
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 ...
Trefoil Knot (CBU)
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...
Hypar (Hyperbolic Paraboloid)
This model, representing a hyperbolic paraboloid, is thought to originate from the paperfolding experiments at Bauhaus in the late 1920’s. However, details o...
Möbius Strip VI “Recycling Symbol” (CBU)
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. ...
Hydrangea Tessellation
Believe it or not, over all these years of folding tessellations, I never folded a clean tiling of Fujimoto’s Hydrangea. I recently decided to make up for th...
Möbius Strip V (CBU)
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...
Hydrangea (Tant)
Another fold of Shuzo Fujimoto’s Hydrangea. I’ve kept two outermost leaf layers free of unnecessary creases. For deeper layers, it becomes much harder.
Trefoil Knot
A trefoil knot from a single Cross Lap Unit.
Cube (BBU E7)
Another cube from BBU-s: 6 × E7, 6 × D4 6 × A1.
Spiked Icosahedron (WASS)
A spiked icosahedron made from Weird Asymmetric Sonobe (WASS) units.
Chrysanthemum
This design is my modification of Shuzo Fujimoto’s Hydrangea. Despite the change being very minor, it allows the model to be shaped in a more three-dimension...
Spiked Icosahedron (Bow-Tie Sonobe)
Spiked icosahedron, folded from my Bow-Tie Sonobe units (also independently designed by tomoko07011209 around the same time).
Lucky Star Fractals (10 different colors)
Ten level-3 Lucky Star Fractals, folded from metallic paper in different colors. This is just a small subset of how many times I have folded this model over ...
Hydrangea
This is, along with Clover Folding, one of the oldest pictures of a tessellation folded by me (taken in June 2015).
Clover Folding
Along with the Hydrangea, this is one of the oldest picture of a tessellation folded by me (taken in June 2015).
Clover Folding (blue)
Along with the other Clover Folding model, this is the oldest picture of a tessellation folded by me (taken in June 2015).
90-Edge Buckyball (PHiZZ Variant IV)
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...
Hydrangea (Prägo Kristall paper)
This is just a simple Hydrangea, designed by Shuzo Fujimoto, but I think it looks really nice in back light. Folded from Grünperga Kristall Prägo, a kind of ...
Two-Unit Cube II
Another simple model in which a cube is built from just two units. See also: Two-Unit Cube I.
Hydrangea from book wrapping foil
Model folded from transparent book wrapping fold which shows the internal structure of the model in an interesting way. Have a look at the detailed review of...
Spiked Icosahedron (Paper Airplane Sonobe)
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...
Fractal Mountains Reflecting in a Lake
A minimalistic self-similar origami design, in the style of Edward Mistretta’s recent works.
Two-Unit Cube I
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 ...
Triangle Recursion
This is the simplest recursive/fractal model I have come up with so far. It is folded from a square. Due to the very high shrinkage factor, which is almost 4...
Twisted Bird Base Fractal
This is a recursion of my Twisted Bird Base Tessellation. The recursive / fractal version looks interesting, but it’s rather hard to collapse.
Lucky Star Fractal (level 7)
This is a level-7 Lucky Star Fractal, the largest number of levels I folded so far.
Lucky Star Fractal Tessellation
This is a tessellation of the Lucky Star Fractal. The standalone star was designed independently by several people, starting with Shuzo Fujimoto. I don’t kno...
Lucky Star Fractal (Open Back)
This model is a variant of the Lucky Star Fractal (aka Logarithmic Star), designed by myself and independently by many others before me, starting with Shuzo ...
Lucky Star Fractal (level 3)
A level-3 fold of Lucky Star Fractal, this time from gray metallic paper. I rarely fold a model multiple times, but this particular model is so nice I have f...
Lucky Star Fractal
This is a recursive version of the Lucky Star molecule. Just like the non-recursive version, it can be tessellated or used for decorating a box. The back of ...
Rhombus Fractal
Rhombus Fractal, an origami tessellation designed by Endre Somos (and independently also by Joel Cooper and by Wei Fu), folded by me. You may also find inter...
Stacked Propellers Tessellation
A refold of my older design, Stacked Propellers Tessellation, this time as a complete tessellation rather than a single molecule.
Phantasma Fractal Variant
This is my variant of Edward Mistretta’s model, Phantasma Fractal. It’s a nice design which can be folded as a single molecule, or tessellated.
Hamiltonian Cycle of Cube
My design for a single-sheet Hamiltonian cycle of a cube. Origami folded from a single long (just above 5:1) rectangle of paper. The bent frame is in typical...
Clover Folding (Fujimoto) and Lookalike (Kosmulski) side by side
A side-by-side comparison of Shuzo Fujimoto’s Clover Folding (left) and my own Clover Folding Lookalike (right). Front and back sides are shown (top and bott...
Clover Folding Lookalike
This is my design which at first glance looks very similar to Shuzo Fujimoto’s Clover Folding but has a completely different crease pattern and design.
Clover Folding (22×22 grid)
I hadn’t folded Shuzo Fujimoto’s Clover Folding for at least two years when I decided to fold one again after seeing some examples beautifully folded by John...
Hydrangea Cube (Harmony paper)
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 ...
Hydrangea Heart
My modification of Shuzo Fujimoto’s Hydrangea into a heart shape. I found on flickr a similar model, designed by Francis Ow.
Lelum Cube
A modified version of Lelum Polelum Cube where one out of each pair of flaps is hidden.
Lelum Polelum Cube
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.
Hydrangea with Leaves
A color-change variant of Shuzo Fujimoto’s Hydrangea, designed by Meenakshi Mukerji. Test fold based on unpublished diagrams, kindly provided by Meenakshi [u...
Stacked Hearts
Stacked molecules of my Hearts Tessellation. This model is a fractal, and you can go on stacking heart upon heart indefinitely, each twice as large as the pr...
Leafless Hydrangea
This Leafless Hydrangea model is a simple modification of Shuzo Fujimoto’s Hydrangea. It’s interesting how a simple change can modify a model’s appearance. J...
FIT (Five Intersecting Tetrahedra), silver
Another fold of Five Intersecting Tetrahedra (FIT), this time with silver metallic paper.
Hydrangea (manuscript pattern)
Happy New Year!
Mesos Logo (Cube-Hexagon Illusion)
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
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...
Purple 90-Edge Buckyball (PHiZZ Variant II)
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...
Spiked Icosahedron (StEM face variant) from Kami
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.
Möbius Strip IV (CLU)
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...
Lotus Cube
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 ...
Stacked Propellers Tessellation (single molecule)
This is a fractalized version of my Propellers Tessellation. Stacked Propellers Tessellation is folded from a 16×16 grid per molecule in this case but you ca...
Six Intersecting Pentagrams (SIP)
This modular woven polyhedron not only looks nice, but it also has a very interesting history of different people designing it independently. Those credited ...
Coaster Cube
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 ...
Flower Icosahedron (StEM)
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...
Cube from Recursive Four-Sink Base
This cube is made from six units, each of which is a recursive four-sink base modified for use as a module.
Fractal Pinwheel Cube
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.
Fractal Pinwheel
This pinwheel displays a fractal pattern with smaller pinwheels embedded inside larger ones, a series which can be continued indefinitely with thin enough pa...
Fenced Tiling of Clover Folding
I designed this tiling of Shuzo Fujimoto’s Clover Folding after I saw the tiling by Peter Budai and thought it would be better to make the borders between mo...
The Tower of Babel
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...
Down the Rabbit Hole
This tessellation consists of concentric square twists of growing size. The medium is self-adhesive holographic foil glued onto tracing paper. The spiral is ...
Spiked Octahedron (WSM)
Spiked octahedron made from my Woven Slit Module (WSM), 48 units from 3:1 paper.
Hydrangea Picture Frame
This picture frame can hold a standard 15×10 cm photograph. It consists of four molecules of the Hydrangea Tessellation (designed by Shuzo Fujimoto), spaced ...
Cube with Depressed Edges (BBU E9)
Made from my Building Block Units (BBU), modified E9 variant.
Hydrangea Icosahedron
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 ...
Cube (3:2 paper, slits outside)
This is about as simple a model as it gets (just 6 units).
Cube (2:1 paper, woven connection, slits outside)
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...
Cube (2:1 paper, woven connection, slits inside)
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...
Cube (2:1 paper, slits outside)
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...
Adjustable Cube
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...
Knobby Cube
Another combination of Building Block Units and tessellations, this time Fujimoto’s Clover Folding, folded without the decorative margin. 18 modules: 6 × BB...
Square Weave Cube
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...
Hydrangea Cube
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...
Clover Cube
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 ×...
Chopin’s Grand Piano (Spiked Icosahedron)
Named after a poem, this model is — strictly speaking — just a spiked icosahedron.
Möbius Strip III (BBU)
A single-sided surface, the Möbius Band is one of the more interesting mathematical objects that can be reproduced in origami.
Makalu
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...
Gasherbrum
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 from StEM modules
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...
Spiked Icosahedron (BBU D2)
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...
Rhombicuboctahedron with Triangular Faces Left Out (BBU D4)
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.
Rectangular Cuboid
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...
Menger Sponge (BBU)
Model uses 192 modules: 120 × A1, 72 × A2
Hamiltonia Cycle of the Cube
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...
Expanded Hexagonal Prism
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...
Cube (BBU E10)
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 (BBU D9)
Cube from 12 modules: 6 × D9, 6 × A1.
Cube (BBU D18)
Cube from 12 modules: 6 × D18, 6 × A1.
Abstract composition “T”
This composition is made from 75 modules: 36 × A1, 30 × A2, 6 × D1, 3 × E4.
Spiked Pentakisdodecahedron (SEU Sonobe)
Compare with the same solid folded from standard Sonobe units.
Icosahedron with Inverted Spikes on all Faces
Compare with an octahedron built using the same technique (octahedron’s page also discusses the technique in more detail).
14-Spoked Wheel
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...
Large Cube
This cube uses PVM Edge Connector Units to create extra distance between the Vertex Modules.
Cube from Sunken Vertex Units
The result of using the sunken variant of PVM Vertex Unit is a cube with four vertices replaced by inverted pyramids.
Truncated Cuboctahedron with Inverted Spikes on Octagonal Faces
This is a physically large model which demonstrates how StEM units made from sheets of different proportions can be combined (obviously, all rectangles’ shor...
Toshie’s Jewel (StEM)
Normally, Toshie’s jewel is made from Sonobe units, but this one is made from StEM units instead.
Spiked Icosahedron (StEM)
In this model, each face of an icosahedron was replaced with a triangular pyramid made from three units.
Spiked Icosahedron (StEM face variant)
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...
Octahedron with Inverted Spikes on all Faces
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...
Menger Sponge, level 1½ (StEM)
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...
Icosahedron with Inverted Spikes on all Faces
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.
Tetrahedron (StEM)
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...
Tetrahedron (SEU Sonobe)
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...
Tetrahedron (SEU from 2:1 paper)
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...
Spiked Octahedron (rotated link method)
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...
Spiked Icosahedron (Sonobe link method)
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...
Spiked Icosahedron (reversed SEU link method)
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...
Spiked Icosahedron (SEU link method)
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...
Ring
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 ...
Rhombicuboctahedron
Compare this model with a version folded from SEU units.
Rhombicuboctahedron
Compare this model with a version folded from StEM units.
Octahedron (StEM, modules pointing outside)
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...
Octahedron (StEM, modules pointing inside)
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...
Octahedron (SEU Sonobe)
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...
Octahedron (SEU from 2:1 paper)
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 ...
Cube (StEM)
This model (second from the left) is compared here with some other simple polyhedra folded from the same kind of module.
Cube (SEU Sonobe)
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).
Cube (SEU from 2:1 paper)
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).
Truncated Icosahedron with Tessellated Hexagonal Faces and Inverted Pyramids on Pentagonal Faces
Made from Tomoko Fuse’s Open Frame II (plain) unit, polyhedron design by me.
Spiked Dodecahedron (SSIT)
See also the same design with different coloring.
Truncated Octahedron (Open Frame Unit)
Made from Tomoko Fuse’s Open Frame I (bow-tie motif) unit, polyhedron design by me.
Menger Sponge (level 2)
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 ...
FIT (Five Intersecting Tetrahedra) in other colors
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...
Spiked Icosahedron
Model folded from a unit I made specially for this purpose.
Spiked Icosahedron
I designed the simple unit used for this model and later learned that it had been already published before by Jose Arley Moreno.
Ticket Menger Sponge
Model folded from Warsaw public transport tickets (back side with magnetic strip visible). 192 modules: 120 for the body and 72 for coating.
Ticket Cube
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.
Truncated Octahedron
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.
Flower Icosahedron (60°)
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.
Flower Dodecahedron (60°)
Compare with an icosahedron constructed from units modified by me in a similar manner.
Spiked Icosahedron (Sonobe variant)
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.
Icosahedron
You can compare this model, which uses straight, unmodified units, with two models made from the same units after slight modification: Flower Icosahedron and...
Umbrella Dodecahedron
The module, originally designed just for folding this dodecahedron, can be also used for other kinds of models. See, for example, this spiked icosahedron.
Poinsettia Ball
Model is placed near a real Poinsettia flower for comparison.
Octahedron (5 levels)
Just like the pyramid, this is a shell with an empty inside.
Golden Ball (Snub Dodecahedron)
The model’s name is a reference to the Golden Sphere from Roadside Picnic.
Decorated Dodecahedron (Penultimate unit)
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...
FIT (Five Intersecting Tetrahedra)
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...
Truncated Cube (PHiZZ)
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...
Modified Buckyball (120 edges)
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...
Jitterbug Icosidodecahedron
You can squeeze this model and transform it into an icosahedron, closing the empty space between units. This is called the jitterbug transformation.
Icosahedron (Penultimate units pointing out)
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...
Decorated Icosidodecahedron
One of the larger models I have designed, this icosidodecahedron has pentagonal faces made up of small triangular pyramids and triangular faces replaced with...
Icosahedron (120° units pointing outside)
See also: icosahedron from same units but pointed inwards.
Icosahedron (120° units pointing inside)
See also: icosahedron from same units but pointed outwards.
Klein Bottle
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)...
Spiked Pentakisdodecahedron (Sonobe)
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 ...
WXYZ
Model is also known as WXYZ Diamonds.
Steinhaus Puzzle
This puzzle, described in Hugo Steinhaus’ book Kalejdoskop matematyczny (Mathematical Snapshots, literally Mathematical Kaleidoscope) consists of six pieces,...
Spiked Icosahedron (Trimodule)
Apart from this basic version, I also made a variant of this model which has additional “fins” on the icosahedron’s edges.
Spiked Icosahedron (Penultimate Unit)
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...
Spiked and Finned Icosahedron (Trimodule)
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.
Spiked Dodecahedron (orange)
See also the same design with different coloring.
Sierpiński Tetrahedron, level 3 (Trimodule)
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...
Möbius Strip II (Trimodule)
This is one of the rather few modular origami designs which use an odd number of units. Compare also with another similar model.
Möbius Strip I (Trimodule)
This is one of the rather few modular origami designs which require an odd number of modules. Compare also with another similar model.
Menger Sponge, level 1½ (Penultimate unit)
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...
Large Icosahedron
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 ...
Koch Snowflake, level 2 (Trimodule)
Compare also with level-1 version of the same fractal.
Koch Snowflake, level 1 (Trimodule)
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...
3D Koch Snowflake (Trimodule)
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...
Blintz Icosidodecahedron
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...