# Modular Balls and Polyhedra

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

Balls and polyhedra are among the most common forms modular origami models take.

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

## Dodecahedron (Penultimate Unit)

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

## 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...

## 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 ...

## 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...

## 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...

## 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...

## 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...

## 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.

## 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...

## 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...

## 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 ...

## 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.

## 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...

## Icosahedron (120° units pointing inside)

See also: icosahedron from same units but pointed outwards.

## 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 ...