Origamic architecture (OA)

Origamic architecture involves the three-dimensional reproduction of architecture, geometric patterns, everyday objects, or other images, on various scales, using cut-out and folded paper, usually thin paperboard. Visually, these creations are comparable to intricate 'pop-ups', indeed, some works are deliberately engineered to possess 'pop-up'-like properties. However, origamic architecture tends to be cut out of a single sheet of paper, whereas most pop-ups involve two or more. To create the three-dimensional image out of the two-dimensional surface requires skill akin to that of an architect.

The development of origamic architecture began with Professor Masahiro Chatani’s (then a newly-appointed professor at the Tokyo Institute of Technology) experiments with designing original and unique greeting cards. Japanese culture encourages the giving and receiving of cards for various special occasions and holidays, particularly Japanese New Year, and according to his own account, Professor Chatani personally felt that greeting cards were a significant form of connection and communication between people. He worried that in today’s fast-paced modern world, the emotional connections called up and created by the exchange of greeting cards would become scarce.

In the early 1980s, Professor Chatani began to experiment with cutting and folding paper to make unique and interesting pop-up cards. He used techniques of origami (Japanese paper folding) and kirigami (Japanese papercutting), as well as his experience in architectural design, to create intricate patterns which played with light and shadow. Many of his creations are made of stark white paper which emphasizes the shadowing effects of the cuts and folds. In the preface to one of his books, he called the shadows of the three-dimensional cutouts created a “dreamy scene” that invited the viewer into a “fantasy world."

At first, Professor Chatani simply gave the cards to his friends and family. Over the next nearly thirty years, however, he published over fifty books on origamic architecture, many directed at children. He came to believe that origamic architecture could be a good way to teach architectural design and appreciation of architecture, as well as to inspire interest in mathematics, art, and design in young children.

Professor Chatani also spent a good deal of time, even after his retirement, traveling to exhibit his work. He frequently collaborated on books and exhibits with Keiko Nakazawa and Takaaki Kihara.

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Maurits Cornelis Escher (17 June 1898 – 27 March 1972), usually referred to as M.C. Escher was a Dutch graphic artist. He is known for his often mathematically inspired woodcuts, lithographs, and mezzotints. These feature impossible constructions, explorations of infinity, architecture, and tessellations. At this site you can find his caleidocycli.

'Caleidocycli" are based on the five convex regular polyhedra (platonic solids):
... tetrahedron - a polyhedron composed of four triangular faces, three of which meet at vertex.
... hexahedron or cube - a polyhedron with six faces (of perfect squares)
... octahedron - a polyhedron with eight faces (composed of eight equilateral triangles, four of which meet at each vertex)
... dodecahedron - a polyhedron with twelve faces (composed of twelve regular pentagonal faces, with three meeting at each vertex).
... icosahedron - any polyhedron having 20 faces, but usually a regular icosahedron is implied, which has eauilateral triangles as faces.

A caleidocyclus is a 3-D ring of tetrahedra. A ring of this kind can be turned continuously through its own centre.

The word caleidocyclus has been extracted from the Greek: kalós (= good) + eidos (= figure) + kyklos (= ring).

The caleidocycli demonstrated here are designed in 1977 by Doris Schattschneider and Wallace Walker and published in 1992 by Benedikt Taschen Verlag GmbH. ISBN 3-8228-0612-9 (dutch version)

You can click below the images of the caleidocycli for a mathematical symmetry analysis of mechanisms in rotating rings of tetrahedra.
A video presentation at YouTube of the rotating rings is also available.


Origami (ori meaning "folding", and kami meaning "paper") is the traditional Japanese folk art of paper folding, which started in the 17th century AD and was popularized in the mid-1900s. It has since then evolved into a modern art form. The goal of this art is to transform a flat sheet of material into a finished sculpture through folding and sculpting techniques, and as such the use of cuts or glue are not considered to be origami.

The number of basic origami folds is small, but they can be combined in a variety of ways to make intricate designs. The most well known origami model is probably the Japanese paper crane. In general, these designs begin with a square sheet of paper whose sides may be different colors or prints. Traditional Japanese origami, which has been practiced since the Edo era (1603–1867), has often been less strict about these conventions, sometimes cutting the paper or using nonsquare shapes to start with.

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About me...

I started with origami in the 1980s. Later on I folded the caleidocycli and boxes of Escher. However, from the moment I saw the OA paper models of Masahiro Chatani I was fascinated and enhanced by it. At first I only made the models of other designers like Masahiro Chatani and Ingrid Siliakus, but nowadays I create my own designs.