# Is it possible to evenly spaced out objects?

1. Feb 13, 2016

### TimeRip496

I can't figure this out. I mean like all the objects(lets take them as a point mass) must be equally spaced from each. The surrounding nearest point masses from each point mass must be equally separated from that point mass. Square grid doesn't work as 4 out of the 8 closest neighbours are separated from the center diagonally, which is longer than the other 4 that are separated horizontally and vertically. I was thinking grid whereby the squares are replaced by circles by I can't seems to figure out. Is there such a thing?

Something like this except the circles are connected and not separated as shown above.

2. Feb 13, 2016

### Nidum

Triangles

3. Feb 13, 2016

### MrAnchovy

Given this and your previous thread you might like to do some background study on packing problems.

4. Feb 13, 2016

### TimeRip496

Thanks! I will look into that.

5. Feb 13, 2016

### Mentallic

Think of which triangles tessellate the most evenly.

6. Feb 14, 2016

### Svein

Bees use hexagons...

7. Feb 14, 2016

### jbriggs444

...with their centers laid out in a pattern of equilateral triangles.

8. Feb 16, 2016

### nasu

You seem to have some unusual definition of closest neighbors. With the usual definition, in the square lattice each point has 4 closest neighbors (or nearest neighbors). The points on the diagonal are next-nearest neighbors.
No matter what the geometry, you will always have next-nearest and next-next-nearest neighbors and so on, which will be at distances larger that the nearest-neighbor distance. Even in triangular or hexagonal lattice.