A reciprocal frame is a three-dimensional assembly of mutually supporting elements.

[1]​.

The principle of structural reciprocity, that is, the use of load-bearing elements to compose a spatial configuration in which they are mutually supported by each other, has been known since ancient times. Its characteristics are:

In the world of construction, the application of the principle of reciprocity requires:

The joining of the elements at the contact points can generally be carried out without mechanical connections, but only by pressure and friction. To support the friction force, there are simple connection techniques such as tying the elements or making notches in the elements at the contact points. Directly dependent on the development of the connections is the deformation of the entire system under load. The increase in slip that occurs with simple joining, such as tying the elements, results in an increase in the deformability of the entire structure.

This type of structures has the ability to span spans (or rather cover surfaces) greater than the lengths of its elements, its geometric arrangement being what makes a stable structure possible. Normally its elements are beam type, although those formed by equal elements can also be accepted as reciprocal structures. As they do not need external support elements, they are used to build bridges, decks or similar structures.[2]​.

Reciprocal structures, also known as Mandala Roof have been used since the century in Chinese and Japanese architecture, as some documents found attest, although very few vestiges of these methods remain.

Perhaps it was Sebastiano Serlio and Leonardo Da Vinci who established the first geometric and structural studies of reciprocity around the year 1500. A clear example of the use of a reciprocal structure can be found in Da Vinci's Madrid codex where the construction of a wooden beam bridge is described (blurred in the central part of the image).[3][4]​.

More recently these structures were used by the architects Kazuhiro Ishii" (the Spinning House) and Yasufumi Kijima"), and the engineer Yoishi Kan") (Kijima Stonemason Museum). Villard de Honnecourt drew sketches showing similar designs in the 19th century, and similar structures were used in the chapter house of Lincoln Cathedral (Lincolnshire, England). It was also used by Josep Maria Jujol in Casa Bofarull and Casa Negre.

The reciprocal roof was developed independently by Graham Brown in 1987 and is becoming a common technique for roofing construction in ecological self-build houses, particularly in modern Rounhouses.[5][6]​.