This talk will be about a project aiming to illustrate geometry using a new family of reconfiguration puzzles inspired by topological and geometric constructions of surfaces. The puzzles inhabit a virtual, rather than physical, world and their "spaces” of possible configurations can be explored through visualization. So far the main outputs are a science centre installation, called Exploratis, developed in conjunction with the Luxembourg Science Centre and Quadratis - Game consisting of 16 puzzles packaged into an app. We will describe both of these, give our motivations (which go back to the interactive book Mathema), and outline the successes, the failures, and some of the problems encountered. Finally, we will attempt to draw some lessons from what we learned along the way.