Geometry. 3d hexagonal map? In simply words:
Square -> cube, hexagon -> ? (figure I don't know)
I want to try to create a 3d map using this figure in application by the similar way as 2d hexagonal.
Are there any such figures except of the one when a hexagonan is simply stretched along the third coordinate? I mean the following:
link
 A: The bitruncated cubic honeycomb also known as the Kelvin foam might work.
A: It depends on what properties you are trying to emulate. However the cuboctahedron is a nice candidate and to some extent the octahedron and truncated octahedron. 
You can fill the plane with squares and also with equilateral triangles and with hexagons. A cube fills space very nicely and the relations to a square are obvious. There are other cell-transitive space-filling polyhedra but not anywhere near the same amount of regularity. Four are: a triangular prism, a hexagonal prism, a rhombic dodecahedron and the aforementioned truncated octahedron which is, to my eye, next nicest to a cube given that the faces are regular and symmetry high. later This answer turns out to be the Bitruncated cubic honeycomb mentioned in another answer. 
Clearly a 3d triangle is a tetrahedron and in the same way that we lop off the corners of a triangle to get a hexagon, a tetrahedron yields an octahedron.
Saving best for last 


*

*The Cuboctahedron has all vertices the same distance from the center as the common edge length, just as a hexagon does. 

*The 24 edges do make 4 equatorial hexagons which is reassuring.

*The 6 vertices of a hexagon can represent the root vectors of the simple Lie Group A2 and the 12 vertices of a cuboctahedron can do the same for A3. 

