Cut & Fold Quasicrystal Blocks

Cut & fold cardstock quasicrystal blocks

A quasicrystal (quasi-periodic crystal) is a structure, real or abstract, that is ordered but not periodic. The building blocks (unit cells) repeat quasi-periodically, not periodically. Quasicrystals can have unexpected symmetries; for example, icosahedral quasicrystals have a kind of five-fold symmetry. You can learn more about quasicrystals elsewhere. There is a good introduction to quasicrystals at The story of the discovery of quasicrystals is told in The Second Kind of Impossible by Paul Steinhardt.

One way to model an icosahedral quasicrystal is with a fascinating set of four polyhedral building blocks with face-matching rules. This four-block model was introduced and described in a pair of groundbreaking scientific papers (which can be found at

You can make yourself a small set of cut & fold cardstock quasicrystal blocks using my downloadable patterns (see below). The polyhedral blocks have face connectors that enforce the face-matching rules.

The four quasicrystal blocks
A small quasicrystal assembly
A small quasicrystal assembly
A small quasicrystal assembly

The patterns are intricate. It takes a lot of time to make even a small number of blocks. They are designed to be cut from cardstock with a laser cutter. If you do not have access to a laser cutter, you can still make a few blocks by printing them on cardstock and cutting them out with scissors and a razor knife.

To learn more about these blocks and how to make them, read this:

Quasicrystal Blocks: Description and Cut & Fold Instructions (PDF)

Then, download the patterns:

Quasicrystal Blocks: Cut & Fold Patterns (zip)

Note: The quasicrystal building blocks are not a general-purpose creative building toy. The connectors are designed to constrain your constructions, not to allow creative freedom.