The first two pieces re-created at his behest closely follow his working blueprint, canning Pickering’s manual approach into a scripting routine and exporting the result to a rapid-prototyping device. Working, for instance, with the brand of geometry pioneered by the British sculptor John Pickering has uncovered unexpected forms of tectonic efficiency. Critically F01(b) secretes an exciting discovery. Inversion is a transformation: it does not create anything new, it just alters what is already there. When the right conditions are met, standard primitives such as planes, cones or cylinders invert into non-standard surfaces, such as spheres, cycloids or cross-caps, without the need to rationalise, triangulate or develop the result. As such, the resulting pieces are little more than copies (or forgeries, depending on one’s point of view) of the original. IJP has worked on three short projects in collaboration with the artist, resulting initially in the production of licensed similes of his original artwork with state-of-the art software and numerically controlled fabrication, with a view to soliciting a grant from the Arts Council in order to rebuild them as large-scale installations in a gallery. F01(b) has two parts, both made of overlapping cones inversed relative to the same centre. In this context circles invert (mostly) into circles, and spheres (mostly) into spheres. Hence, rather than recasting the static geometry favoured by the artist in a new technical idiom, deploying the analytic equations of inversion in F01(b) opens up the possibility of a contemporary reevaluation of his modus operandi itself. However, unlike the standard polar variety (which must be rationalised through triangulation if it is to be built), these spheres are made of flat quadrilaterals. Geometry and algebra, the study of figures and that of symbols, separated more than 400 years ago; as noted in the introduction to this issue, this separation lies at the root of mathematical modernity, and reminds us that unlike art history, or even technology, progress in mathematics is extremely fast paced. Planes invert into spheres too.