Is it possible to evenly spaced out objects?

[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.

 

[Nidum]

Triangles

 

[pbuk]

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

 

[TimeRip496]

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

Thanks! I will look into that.

 

[Mentallic]

Think of which triangles tessellate the most evenly.

 

[Svein]

Bees use hexagons...

 

[jbriggs444]

Bees use hexagons...

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

 

[nasu]

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?

View attachment 95750
Something like this except the circles are connected and not separated as shown above.

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.