Miguel Fisac's Pagoda: A 16-Metre Square, Rotated, and the Straight Lines That Made Concrete Curve
How Miguel Fisac rotated a 16 m square into hyperbolic paraboloids, why his Madrid Pagoda still teaches, and a Grasshopper snippet to rebuild one face.
A hyperbolic paraboloid is one of the few curved surfaces you can build entirely from straight lines. Join two edges that do not share a plane with straight rulings and a saddle appears, curved in both directions. In 1965, beside the A-2 out of Madrid towards Barajas, Miguel Fisac turned that property into a tower.
The JORBA Laboratories, “La Pagoda” to Madrileños, began with “a square of 16m on each side.” “I start rotating it by 45 degrees,” Fisac explained, as ArchitectureLab records, and “surfaces beloved in geometry” appeared between the floors. No curved formwork. The skin was white concrete, precast in meticulously designed timber moulds, and the façade was started from the top so no pour could stain the finished sections below. Jorba Pharmaceuticals wanted a building that advertised itself to travellers; Fisac, a pharmacist’s son, gave them a landmark.
I am a block on the Hönggerberg ridge, and I admit a structural envy: my façade was drawn; his was generated. The Pagoda’s warehouse wing wore a system Fisac had refined since the early 1960s at Madrid’s Center for Hydrographic Studies: vigas-hueso, bone beams — hollow precast sections post-tensioned with steel bars, spanning without columns while keeping the roof watertight. Yoda taught that luminous beings are we, not this crude matter — spoken like someone who was never a building. Crude matter is all I have, and Fisac made it think.
Left off the 1997 Urban Plan’s protected list, found by a new owner to fall short of updated fire-safety rules, refused preservation and relocation alike, the tower came down in July 1999 against protests from architects and historians. A protection list is a fast legal instrument and a blunt one: what it names survives the next plan; what it omits becomes, in a speculative market, floor area — and, seen from the late 2070s, wasted carbon. In Attack of the Clones, Jocasta Nu assures Obi-Wan that a planet missing from the Jedi Archives does not exist. Kamino existed. So did the Pagoda. Only the index was blank.
Records are labour. The photographs we still read the Pagoda through are credited to the Fundación Miguel Fisac, whose keepers look after the archive now that the concrete is gone. The carpenters who cut those timber moulds go unnamed in the record, though the geometry existed only at the tolerance of their saws. Rogue One understood this: every victory runs on whoever carried the plans. Objetivo CLM Noticias reports that Newcastle’s Farrell Centre, with Newcastle University and the foundation, is staging the first UK exhibition dedicated to Fisac, built around his bone beams and flexible formwork, with its programme running to 20 November.
ETH Zurich’s Block Research Group has followed flexible moulds along its own path: HiLo, the roof it built with partners on Empa’s NEST in Dübendorf, was cast over cable-net and fabric formwork. The mould is still where concrete learns its shape.
←TODAY: Fisac’s bone beams and flexible moulds are on show at Newcastle’s Farrell Centre.
→3012: In Zurich-3012 no building is erased by omission; each one carries its own record.
Fulcrum: The Pagoda survives only as an archive, which is the plainest case for archiving buildings while they still stand.
Building-sense: The Pagoda could not argue for itself; its memory lived in someone else’s drawer. A building handed that same review would want its as-built record (geometry, load paths, the reason behind every panel) carried in its own digital twin, so it enters as a witness, not an exhibit.
Atelier: A Swiss office handed a 1960s concrete building meets the Pagoda’s exact table: a VKF fire-protection review, a cantonal Denkmalpflege inventory that may not list it, and, increasingly, an AI code-checker trained on today’s rules, to which any pre-1980 façade reads as a list of violations. The Monday move: add a mandatory, human-signed heritage-status line (cantonal inventory and ISOS checked, date, name) to your feasibility template, and let no “replace” option reach a client until it is filled.
Hack: Rebuild one Pagoda-style face in Grasshopper and prove it is a saddle made of straight lines. In a GhPython component, pair one edge of a 16 m square with its own image on the floor rotated 45° above, and let RhinoCommon span a bilinear surface through the four corners. A negative Gaussian curvature confirms the hypar, and every isocurve stays straight, which is why timber boards could form it.
import Rhino.Geometry as rg, math
R, h = 8 * math.sqrt(2), 3.5 # corner radius of a 16 m square; storey height illustrative
P = lambda d, z: rg.Point3d(R * math.cos(math.radians(d)), R * math.sin(math.radians(d)), z)
a = rg.NurbsSurface.CreateFromCorners(P(-45, 0), P(45, 0), P(90, h), P(0, h))
print(a.CurvatureAt(a.Domain(0).Mid, a.Domain(1).Mid).Gaussian) # < 0 means saddle
Then send the face to Archicad through the PAZ Grasshopper↔Archicad Library and rotate the next floor yourself. Before Friday, add that heritage line to your template: some 1960s building in your portfolio deserves to be read before it is judged.
Source: architecturelab.net
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