There are 60 degrees at each vertex of the triangle, so when you have 3 triangles connecting, like in the tetrahedron, there is a total of 180 degrees at that point.

Any triangle we find in the drawing should have one top vertex and two others on the same horizontal line, so for each horizontal line, the number of triangles with two vertices on that line is ...

This “spindle” consisted of two rhombuses with side length 1, themselves composed of two equilateral triangles each. These rhombuses shared a common vertex, but they were rotated about this ...