Exploration in Geometry: Exhibition and Polyhedral Workshop

This exhibition introduces a variety of geometric paper-made polyhedra, each built of variations of a single building unit. This building unit is one of eleven known net of the octahedron, and was named Octafold by Tamir Ashman, developer of a magnetic geometric model, which is also an innovative pedagogical model for teaching spatial geometry. Lying at the heart of this model is the Octafold (Figure 1), which allows for a rapid and intuitive folding of complex polyhedral structure, without the need of formulas, angle computations, scissors, or even glue. Nor does it require any prior knowledge in geometry.
The uniqueness of the Octafold is in its power to unify the folding and unfolding patterns of entire series of polyhedra.Thisexhibition presents only five possible series of the Octafold, each characterized by a different type of Octafold tessellation


Some of the structures presented in the exhibition are significant in the fields of molecular biology as well as classiandmodern architecture, while others have yet to receive their scientific name.

"It is really surprising how much enlightenment will come following the construction of the models rather than preceding it, and once you begin making them you may find that your enthusiasm will grow", said Father Magnus J. Wenninger with respect to polyhedron models in his book Polyhedra models. An experiential workshop accompanies this exhibition embodying these words of Father Wenninger. During the workshop visitors may explore, in pairs or small groups, this versatile and significant field of polyhedral structures. By using large folding units, visitors will learn and experience the principles of the model and will structure a various polyhedra in a quick and playful manner. This is a joyful experience, instilling in participants feelings of achievement and fulfillments alongside increased curiosity.

Exhibits Samples

Discovering the Octafold building unit

The Octafold was discovered through explorations of the stella octangula, also known as

מרכבה נפתחתמרכבה נפתחת 2מרכבה עם אוקטהדרון

מרכבה מנייר

The unified net for polyhedral srtuctures

להמשיך לקרוא

תמיר אשמן מציג את יחידות ה – octafold בליל המדענים 2014 – אוניברסיטת תל אביב

חגיגה של משחקי קיפול נייר בליל המדענים באוניברסיטת תל אביב. מאות ילדים קיפלו מבנים תלת מימדיים מורכבים מיחידות בניה דו ממדיות מנייר. לומדים גיאומטריה בצורה חוויתית וכיפית.

תמיר אשמן מרצה על המודל הגאומטרי שפיתח בליל המדענים 2014

תמיר אשמן מרצה על המודל הגאומטרי שפיתח בליל המדענים 2014

הרצאה של תמיר אשמן בליל המדענים

הרצאה של תמיר אשמן בליל המדענים

ילידים והורים לומדים גיאומטריה בצורה חוויתית

ילידים והורים לומדים גיאומטריה בצורה חוויתית


A Playful Geometry Workshop: Creating 3D Polyhedral Structures

A Playful Geometry Workshop: Creating 3D Polyhedral Structures.

Polyhedral structures play a significant role in our lives, of which we are typically unaware. We live in Platonic cubes, we are awestruck as we look at the Egyptian pyramids, and the viruses

octahfold units

octahfold units

we catch are, in fact, living icosahedrons. Physical atoms from which are world is comprised are drawn to polyhedral structures. Polyhedral structures bring together varied fields of knowledge, such as art, architecture, molecular biology, and mathematics. They were a source of fascination to polymath artists such as Leonardo Da Vinci (1452-1519) and Albrecht Dürer (1471-1528), architects such as Buckminster Fuller, and researchers such as Nobel prize laureate Dan Shechtman who had studied these structures. Yet, have we have learned about polyhedral structures in school? Have we ever built them with our hands? Held them? Sensed them? Have we ever built a geodesic dome? Heard about the rhombohedron or the decahedron? Had we ever experience the spiritual beauty of the stella octangulla or the aesthetics simplicity of the octahedron?

To date, any such attempt would have required complex mathematical calculations. Lacking the availability of simple pedagogical tools, it was impossible to investigate, simply and joyfully, this rich world of polyhedral structures that comprise our world, and our own beings. Most of us had never had the opportunity to hold an icosahedron in our hands and were deprived of the spectacularly aesthetic world of significant multidimensional structures. Workshop participants will fold polyhedral structures, simply and quickly, to form an extensive series of paper polyhedral structures. The game and workshop are developed on the basis of a single paper folding unit comprising eight equilateral triangles

This octahedral paper folding unit conjoins with other such units or segments thereof, creating an infinite range of two-dimensional nets that may be folded in a series of varied polyhedral structures. This paper folding game thus demonstrates the power of one specific form of octahedral net comprising eight equilateral triangles, one of 11 known nets of the octahedron, in explaining a specific series of polyhedra
This workshop allows participants to get acquainted with the world of two-dimensional nets and the historic evolution of this field from the 16th century, the time of Da Vinci and Dürer, until our time. Participants will experience first hand the folding of two-dimensional nets into complex structures using a simple new technique. This technique overcomes the need of mathematical formulae or angle computation. It even forsakes the need for glue or scissors. No previous knowledge is required of the folded polyhedral structures, which reveal themselves through the folding process. This simple pedagogical tool may serve math teachers of in their endeavors of teaching spatial geometry . Moreover, the model presented herein unifies most polyhedral structures by unfolding them into a single net of a single cut.
workshop is suitable for both small and large groups of children and adults, starting at he age of 7. This experiential workshop is not only educational and fun but also serves to develop participants sense of achievement.