What is the structure of the matter

The simplest structure can be constructed from the simplest objects. In 4D space (while we can imagine it in our minds) the simplest obkect is 4D sphere. If we take these spheres as the basix unots the question is arise - Is there the most dense packing can be made from it?

It is known that the most dense packing in 3D space is the hexagonal and face centered cube lattices and the icosahedron as the single unit of the nearest sites. We don't know whether the structure like the icosahendon with the pentagonal symmetry exists or not in 4D space. It is more probable that such structure not exists.

It is interesting to compare the most tight arrangment of the spheres in different dimansions. It was made in my brief paper On the structure of 4D medium (in Russian). The analysis in it shows that the movements of the nearest spheres demanded to penitrate the sphere through them in 4D space is the less than in 3D and 2D spaces. It can be treated as the versatile structure is in 4D space. The sites of the 4D lattice made from the 4D spheres can move through the lattice with the less energy expenditures then the correspondent sites in spaces of low dimensions.

We had been called the 4D spheres the apeirons in our previous works.