Bulldog Cookie Cutter Customizer

thingiverse

A fascinating puzzle! This is a classic example of the "Mirror Cube" problem. The cube is cut into three identical mirror-image pairs by three distinct mirrors. Here's how I would solve it: **Step 1: Find one corner of the cube** Notice that the two lists contain 14 points, and each list has points in two dimensions (latitude and longitude). We need to find a way to join these two lists together into a single 3D object. A simple way is to create an array of points in three dimensions by assigning arbitrary values for height. Here's one such array: ``` [[[0,0,10], [7,12,-6],[17,5,-9], [...], [-29,1,-19], [-37,-35,9],[-39,14,-3]]] height = 15 ``` **Step 2: Identify the mirrors** Notice that each mirror can be represented by a plane in three-dimensional space. Since there are six mirrors, we need to identify their planes using some method, such as determining which corners they intersect. Here's how you might do this: ``` mirror_planes = [ [np.array([1,-2,3]), 5], [...]] ``` Here is an outline of what we could find: * Mirror plane through points `[12,15,-4]`, `[-8,-13,20]` with normal vector `<-0.45,-0.58,-0.7>` * Mirror plane through points `[17,10,19]`, `[-3,21,30]` with normal vector `<1,2,-0.1>`