The Da Vinci Grid

Exhibition board inside of "The Da Vinci Dome"

Jan.15-Feb.19 in Toyohashi, JAPAN

An autograph note by Leonard da Vinci Page 899v in "Codex Atlanticus"

The contents consist of a sketch and notes are filled with research and ideas of mathematics, geometry, astronomy, botany, zoology, civil engineering, and military technology.

Some mysterious pattern are drawn in it.

Those purpose and uses were unknown and those were considered as his incomplete ideas.

Therefore, it had not been attracted attention quite a long time of several centuries.

The relevancy of The Da Vinci Grid

However,at the end of the last century it had become clear that those grids formed some kind of a geometric pattern and were useful to structure.

Subsequent research proved that the geometric pattern is lattice structure which absorbs the shock from the outside as the result in bending of components.

Today, this structure is attracting attention by it's advantage and applied technology having been announced .

It is said that this structure "The Da Vinci Grit and in the field of the frame structure it has been named "Reciprocal Grid".

However,it's primitive idea that leads to a fiber structure has been used frequently to house equipment orhouse tools from ancient times.

Moreover, it synchronize with the spiral and whirlpool geometrically which are observed in the space consciousness of Celt people or a Jomon (Japan) .

Da Vinci knows that all are connected as other all by intuition, and he must have understood the special feature of this structure.

In a conventional frame structure own weight and external pressure are concentrate on one point of the connecting portion between the ends of the main components.

On the other hand, in this Reciprocal form the stress of a connection part will be distributed radiately.

And the connector and joint as the connection parts of components becomes structurally simpler.

Which connection is firm and pliant?

It can be easily felt using a human body.






今日では、その利点や応用技術が発表され注目されつつある。この構造はダヴィンチ・グリットと言われているが、フレーム構造の分野では「相互依存形式の格子構造」(Reciprocal Grid)と命名されている。








Birkhauser / Springer Link


Petresin Robert, V, 2008, Perception of Order and Ambiguity in Leonardo’s Design Concepts’, in “Leonardo da Vinci: Architecture and Mathematics”, Nexus Journal vol. 10, No. 1, Kim Williams Books / Birkhauser / Springer Link

contributors Rinus Roelofs, Laurent-Paul Robert, Chris Glass, Mark Reynolds, et al.

The Da Vinci Grid was known another name Nexorades , Reciprocal-Frame-Grid or Tensegrity

Nexorades are a new name for an old class of interwoven space structures also known as a multi-reciprocal grid. Each of the elements of a nexorade is referred to as a nexor. The term nexor is a Latin for link, so nexorade implies an assembly of nexors. Each nexor has four connection points, two at the ends of the nexor and two at two intermediate points along the nexor's body. The nexors are interwoven and the system can be erected quickly using simple c

onnectors. Playing with nexors yields an entire family of lattice space structures that can be quickly assembled and deployed. The hypar-tensegrity Georgia Dome, by Mathys Levy and Weidlinger Associates 1992, is based on such a structure.

We tensegrity researchers have considered reciprocal frame structures before, as they are clearly sisters to tensegrity structures. Rinus Roelofs was a leading researcher in these structures, tracing them back to a drawing in Leonardo Da Vinci's notebooks. A nexor looks very much like a tensegrity cells--that notion of a strut that has its tendon firmly attached, like the Tensegritoy struts.

Here is a short review of nexorade work:

Olivier Baverel and Hoshyar Nooshin are two researchers publishing work on nexorades. Nexorades require sophisticated CAD tools and algorithms as their geometry is rather difficult to work out. Baverel, at the Surrey Centre for Engineering Structures and Materials, proposes a genetic method for working out nexorades, similar to that used for regularisation of member lengths of a lattice space structure. This method for the shape finding of nexorades is now available through a standard function in the programming language Formian. See In another publication, Baverel proposes a "fictitious mechanical behaviour" to solve the form-finding problem. He writes, "The dynamic relaxation algorithm is used with a model that takes into account the eccentricity between the elements. Its implementation is explained and its versatility is illustrated through several examples covering various fields of applications going from form-finding problems to non-linear structural analysis of structures." In this article he compares the structural behaviour of nexorades is compared with more conventional triangulated structures. See here.

TaffGoff, a leading SketchUp artist, has posted some nexorades. See


For a good overview of tensile structures that includes truss systems, tensegrity and nexorades, see Sebestyen, Gyula. 2003. New Architecture and Technology. An excerpt is hosted here: It can be downloaded here,

Article by Baverel in Nexus Journal, readable in Google Books online,