The 12 vertices of a regular icosahedron can be interpreted as 12 equally spaced rays from the origin headed out into space toward infinity, a spiky icosahedron.
Other shapes possible, including tetrahedron, octahedron, square antiprism, and snub cube. Tammes problem. Coordinates from Neil Sloane. Ray tracing by Hugo Pfoertner.
The number of vertices of an icosahedral geodesic grid is A005901, or 10*n^2+2 (convenient in base 10). Curiously, the solution for 42 is not geodesic, not possessing the symmetries of an icosahedron. Possibly for similar reasons why the square antiprism is superior to the cube. (Also vaguely related to geodesic domes: Kobbelt subdivision sqrt 3.)
No comments :
Post a Comment