By 1970, the year Uglow produced Polygons, he had embraced ever more purist systematic processes of applying internal geometry to his works. At the heart of Uglow’s painting was a prolonged investigation of conceptual problems of perception and, what Brendan Prendeville has termed, a “virtual reinvention” of perspective “unprecedented in its severity, its absoluteness”. In his studio, Uglow would construct miniature stage-sets or set-ups, for still lifes and nudes alike, designed to scrutinise his own powers of observation. In Polygons, its mathematical premise adamantly stated in the title, objects from the everyday subjected to Uglow’s ruthless conceptual and intellectual examination. As Martin Golding argued, “It must be made; and before that, it must be thought.”

We see the construction through extreme perspective, viewing the table as though from below with the creamy shelf, the same surface as in Still Life with Honeysuckle, 1968, cat. no. ???, receding away dramatically. The intimate scale of the picture demands close scrutiny of the geometry of composition, of the refined colour palette, and of Uglow's brushwork. Inscribed marks track minute changes in placement of the trio of objects as Uglow experiments with establishing an ever so slightly disquieting internal order of subtle asymmetry heightened by falling shadows. Local and unmodulated colours dominate the picture: the orange of the wall is picked up in the lid of the cigar box whilst the creamy table top is repeated in the lid of the pill box. Uglow's idiosyncratic, fresco-like, cornflower blue pierces with a certain acid coolness through the warmth of these localised areas of colour. Individual brushstrokes are barely distinguishable with Uglow handling the paint with delicacy, pristinely preserving a smooth surface.

As with Still Life with Cast, 1960, Uglow acknowledges the precedents of the still life genre in Polygons, introducing the moralistic undertones of vanitas and memento mori into the modern day setting of the twentieth-century artist’s studio. The cigar box and pill box hint at pleasure and pain of life, the vices and indulgences, not just those of the body but also the seductive beauty of a painting for the eye. Uglow transforms the legacy of still life into a rigorously contemporary endeavor, compelling figurative painting towards radical innovations. When asked the objective of his work, Uglow replied, “I’m trying to make something new.”