Emit an isometric cube as three SVG polygons and test its shared edges

An isometric cube is constructed from three SVG polygons that must align along equivalent edges. A single vertex deviation of even one user unit can result in either gaps or overlaps. This script generates the three faces with integer coordinates and validates the edges before accepting the SVG output. Points are given alphanumeric labels, with the entire geometry centered around a point (100, 100) and two offset values derived from cx, cy, dx, and dy.

The seven points involved are labeled C, T, B, UR, LR, LL, and UL. Each face of the cube is represented as a list of these point names. For a 30-degree edge with a vertical rise of 50 units, the exact horizontal displacement is calculated as 50 * sqrt(3), which evaluates to approximately 86.603, and is rounded to the nearest integer, 87, to ensure all coordinates are whole numbers.

This rounding results in a slight deviation from the true 30-degree angle for the slanted edges. The script imports necessary modules, sets key variables, and prints a detailed internal representation of the cube's coordinates. The program proceeds to define functions to process these points into rings and edges of each face, calculates the area of each face, and verifies that all faces collectively form a hexagon.

It checks that each edge is shared by exactly two faces, and confirms that the combined areas of the faces match the area of the hexagon, ensuring the cube tiles the hexagon correctly. Finally, it identifies and lists the edges that are unique to the hexagon, ensuring no edge is used more than twice, maintaining the structural integrity of the isometric cube.