   stereometry
  Hi, I am trying to come up with an algorithm to generate an array of 3D points. The adjacent points should be within a same distance to each other and fit in a given sapce (for example in a sphere).2D example:any tips or help appreciated.   
  It depends on when you consider points adjacent, but from your picture, it seems that you really want to fill space with polyhedra, where the points are adjacent if they are vertices of the same polyhedron. The only polyhedron where all vertices are of equal distance to each other is the regular tetrahedron though, and according to this page, filling space with regular tetrahedra is in fact impossible.   ;  Is the center of each cell of the Rhombic dodecahedral honeycomb 3D tesselation the same distance from each neighboring cell? -- I'm not sure but they might be. Anyway, that space-filling tesselation is the closest "in spirit" to the hexagonal tiling of the plane, so might be of interest to the OP.   ;Quote:Original post by jwezorekIs the center of each cell of the Rhombic dodecahedral honeycomb 3D tesselation the same distance from each neighboring cell? -- I'm not sure but they might be. Anyway, that space-filling tesselation is the closest "in spirit" to the hexagonal tiling of the plane, so might be of interest to the OP.The wikipedia article says that it's dual (so the centers as vertices) is a honeycomb of tetrahedra and octahedra, and for an octahedron, the distances between two vertices on the same face, and the distances between opposite vertices are different.   ;  Thanks for replies,I expected to fill space with tetrahedra (or maybe icosahedra), but didn't realised it's impossible.   ;  Actually, the only 3D space-filling tessellation I can think of that definitely has the property that each cell is the same distance away from each of its neighbors (on faces) is cubes, which is pretty boring. Are there any other 3D tessellations that have this property?   ;  I believe angle between faces of polyhedra should divide 360 without reminder than tesselation is possible.Cube - angle between faces 90 deg.Tetrahedron - angle ~70.5.   ;Quote:Original post by jwezorekActually, the only 3D space-filling tessellation I can think of that definitely has the property that each cell is the same distance away from each of its neighbors (on faces) is cubes, which is pretty boring. Are there any other 3D tessellations that have this property?If you extrude any 2D tesselation with this property by the right amount, you can make the 3D tesselation have this property too, so prisms for example will work too.   