This book is both a collection of origami tessellations and a manual of design for them. In general, a tessellation is a plain work covered with geometric patterns (called a "base part"), and an origami tessellation is a geometric pattern created by folding a single sheet of paper, similar to a tessellation. The 'design' of an origami tessellation refers to the process of constructing a crease pattern on paper prior to folding. General crease patterns are covered by a base part consisting of crease lines connecting the points of a square or triangular lattice.
The book begins by explaining such general design methods, the history of origami tessellations, and the geometric features of flat origami. The book then proposes and introduces a new design method: the "twist-based design method." The method generates base parts that connect "twist patterns" (that can be folded with a twist) without using a lattice. Therefore, it can generate base parts such as regular pentagons, which cannot be generated with more conventional methods, and can generate new origami tessellations connected them.
Features
- No proofs or formulas in the text and minimal jargon
- Suitable for readers with a roughly middle school to high school level of mathematical background
- Web application implementing the method described in this book is available, allowing the readers can design their own patterns.

Yohei Yamamoto is a researcher of Information and Systems at University of Tsukuba. He received his Ph.D. in engineering from the University of Tsukuba in 2023. He has been present post since April of the same year. His research interests center on origami design and geometric modeling techniques. The origami artworks created by him have features that are geometric flat shapes. In addition to his research activities, he is actively involved in outreach activities such as the sale of his works and the organization of workshops.

Jun Mitani is a professor of Information and Systems at University of Tsukuba.

He received his Ph.D. in engineering from the University of Tokyo in 2004. He has been present post since April 2015. His research interests center on computer graphics, particularly geometric modeling techniques and their application to origami design. The origami artworks created by him have features that are three-dimensional shapes with smooth curved surfaces. His main books are "3D Origami Art (2016)" and "Curved-Folding Origami Design (2019)". In 2010, through an exchange with ISSEY MIYAKE, he contributed to the launch of the new 132.5 fashion brand. He also cooperated in the design of origami used in the movies "Shin Godzilla (2016)" and "Death Note Lightup the NEW world (2016)". His unique origami has been well received around the world and he had received invitations to hold workshops and exhibitions in Germany, Switzerland, Italy, Israel and many other countries. His work had inspired the design of the trophy for the Player of the Match winner of each game at the Rugby World Cup 2019. He was appointed as a Japan Cultural Envoy from the Agency for Cultural Affairs and travelled to eight Asian countries to promote cultural exchanges through origami in 2019.