Euler CAD 9.0

Euler CAD 9.0 is a small app I created with Gemini AI using cubes as componets to construct structures. It uses the Euerl formula E-F+F-S=1 where S is a solid in the Euclidean sense. In addition during augmentation Liebnitz's Law applies to the effect that two objects cannot occupy the same located at the same time are therefore in this context are counted once. The app also features the ability to delete vertices, edges, faces, and solids. When this is done the app automatically accounts for the absent components and recalculates the formula summing both what is present and what is absent. The net result is that the universal invariant of 1 is preserved troughout. 

One other feature is that during closure as when constructing a toroid composed of 8 cubes, the app counts the missing componets in the center as absent are adjust the formula accordingly. Unfortunately, the app does not do so for Stewart toroids or toroids with large holes. 

This is a minimal viable model. It is intended to illustrate how a it might be incorporated into a more sophisticated program like Great Stella by Robert Webb.