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Torre Espacio

Pei Cobb Freed & Partners

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Pei Cobb Freed, Pei Cobb Freed & Partners Architects LLP

Project Name

Torre Espacio

Project Status


Year Completed



120,250 sq. meters


Torre Espacio Castellana S.A.; Grupo Villar Mir

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Project Description

Torre Espacio occupies an exceptionally privileged site on the most important avenue in Madrid. The program consists of 43 office floors, two corporate floors at the top of the tower, three floors of commercial space at the base of the building, and six levels of underground parking. Besides providing efficient and attractive offices, as one of its city's most prominent buildings it will energize the space in which it stands and animate the skyline of Madrid.

The design of Torre Espacio evolves from a square plan at its base to a gently curved lozenge, shaped by the intersection of two quarter circles, at its crown. Were this a work of sculpture, such a form could readily be carved from a solid block of stone. But as a work of architecture, its intersecting curved surfaces are necessarily composed of many separate panels that must be individually fabricated and assembled. Hence, there was a need to discover and adopt a geometric order that can rationalize and facilitate the desired evolution from square to quarter circle. We have found this order by subdividing the building section into 44 horizontal layers and then subdividing each quarter circle of the plan into an equal number of radial segments. The intersections of successive layers in section with successive segments in plan define points along a vertical curve. Because the mathematical formulae describing this curve are based on the cosine, we call it a cosine curve.

An important characteristic of the cosine curve is that while it simplifies fabrication and assembly of the curtain wall, its rate of curvature is not constant but rather changes gradually over its entire length. This gives the resulting tower form its distinctive and visually appealing sense of energy, almost as if it were a living organism that has sprung from the earth on which it stands.
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