Figures for "Gaudí's strange geometry"
Figure 1. The tower at Park Güell, a trencadís chimney pot at Güell Palace, and the abelian sculpture study in the Sagrada Familia museum.
Figure 2. A cube and four basic operations applied to it: relax, sag, smooth and twist.
Figure 3. Triangle pair forming an elbow (left) and the corresponding hypars (right).
Figure 4. Dodecahedron, stellated dodecahedron, hyparhedron and smoothed figure.
Figure 5. An octahedron with four relaxed edges and a cube with two pairs of relaxed edges.
Figure 6. Fractal development of the tetrahedron.
Figure 7. Relaxed version of the tetrahedron fractal.
Figure 8. Basic structure of the abelian study (top), relaxed and sagged to give its final form (bottom).
Figure 9. Spiral extrapolation of the abelian study.
Figure 10. Twisted primitives: tetrahedron, icosahedron and cube (90° and 180° twists).
Figure 11. Two twisted columns combined and smoothed to approximate the shape of the Park Güell tower.
Figure 12. Two twisted, smoothed and tiled columns bent to form interlocking torii.
Figure 13. Four tiled bands twisted around logarithmic spiral surfaces, sagged (left) and inflated (right).
Figure 14. Alexander's horned sphere, twisted and tiled.
Figure 15. Approximating a hypar with a subdivision surface.
Figure 16. Faux-tiling texture using POV-Ray.