# Balls and Polyhedra

Models of this type are also automatically listed in: abstract, geometric, mathematical object More restrictive types: cubes and cuboids, modular balls and polyhedra, modular cubes and cuboids, other modular polyhedron, other polyhedra, single-sheet cubes and cuboids, other single-sheet polyhedra

Models representing all sorts of polyhedra, including roundish ones (spheres and other smooth shapes can mostly only be approximated in origami).

## Icosahedron from Strip (CFW 260)

This is one of many polyhedra from a single sheet designed by Shuzo Fujimoto. It is folded from a long strip, somewhat shorter than shown in the CP in the bo...

## Truncated Octahedron with Square Faces Concave (CFW 255)

This origami shape, designed by Shuzo Fujimoto, is a truncated octahedron, but with the square faces replaced by inverted pyramids. It is folded from a singl...

## Dodecahedron (Penultimate Unit)

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

## Cube (Penultimate Unit)

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

## Cut Surfaces of a Cube (CFW 339)

This interesting model by Shuzo Fujimoto represents a cube with a corner cut off. Depending on the proportions of the paper strip used, the cut surface is cl...

## Cuboctahedron (Open Frame Unit)

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...

## Two-Unit Cube III

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...

## Tetris

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 ...

## Octahedron with Concave Faces (CFW 226)

This polyhedron is like a regular octahedron whose each face was replaced with a triangular pyramid pointing inwards. The three faces other than the base are...

## 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...

## 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...

## When Rebecca Met Shuzo 2 (Opus 702)

The name of this design by Robert Lang is a little origami joke. It references two creators, Shuzo Fujimoto and Rebecca Gieseking, and it does indeed combine...

## Regular Octahedron (CFW 246)

A regular octahedron from one sheet, by Shuzo Fujimoto. This design is very paper-efficient, and surprisingly sturdy given how little paper is wasted on the ...

## 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...

## Cube (BBU E7)

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

## 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...

## Two-Unit Cube II

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

## 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 ...

## 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...

## 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 ...

## 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.

## 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...

## 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...

## 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 ...

## 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.

## Cube with Depressed Edges (BBU E9)

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

## 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...

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...

## Name Plate / Kusudama Stand

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 (stacking variant)

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...

## Name Plate (candy wrapper variant)

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

## Bumpy Octahedron

Some recent cube stands by Owrigami reminded me of my PVM unit and I got the idea of combining several of them on a single sheet of paper. This model is esse...

## 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 ×...

## 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...

## 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.

## 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.

## 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...

## 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...

## 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.

## Truncated Octahedron (Open Frame Unit)

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

## 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.

## 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...

## 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...

## Steinhaus Puzzle

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

## 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 ...