## Spiked Icosahedron (Checkered Sonobe)

Spiked icosahedron, folded from my Checkered Sonobe units.

This page lists modular origami models made from a medium number of units (more than 12, not more than 90).

Spiked icosahedron, folded from my Checkered Sonobe units.

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 ...

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

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

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...

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

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...

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...

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

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

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...

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.

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...

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 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...

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

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 ...

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...

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 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.

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...

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...

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 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.

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...

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.

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...

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 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...

Compare this model with a version folded from SEU units.

Compare this model with a version folded from StEM units.

See also the same design with different coloring.

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

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.

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.

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...

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...

See also: icosahedron from same units but pointed inwards.

See also: icosahedron from same units but pointed outwards.

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.

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 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.

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

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...