rhombic dodecahedron

Replies to This Discussion

Permalink Reply by Nik Willmore on February 5, 2016 at 12:27am

A "chain of cubes" may not resolve in any way to the way the rare space-filling aspect of rhombic dodecahedron.

Is it just skewed?

BECAUSE 3D XYZ SPACE AFFORDS CUBE PACKING, that means all 3D packing is based on cubes, and thus a rhombic dodecahedron must be basically a hidden cube network.

Or, not. Any molecular crystal structure that fills 3D space distills down to a "unit cell," but that doesn't necessarily constrain the inner geometry to anything cubic.

So what is the "unit cell" of rhombic dodecahedral packing?

It's ABABAB...stacking, where A-B-A creates the edge of a cubic cell:

Here I try to define a cube:

So there must be many rhomboids in a single 3D XYZ packing, and thus so no, "a (single) cube" does *not* deform into a rhomboid, but more like the guts of a cube does that.

Permalink Reply by Dana on February 5, 2016 at 1:52pm

thanks nik , 

please forget the previous one  ... simply , if i have one row of cubes ... And I need to change the cubic shape  gradually to Dodecahedron .. what is it the definition ?

http://en.wikipedia.org/wiki/Dodecahedron

 http://en.wikipedia.org/wiki/Rhombic_dodecahedron#mediaviewer/File:...

and thank you so much again 

dana 

Attachments:

• cubes-156905_640.jpg, 77 KB

Permalink Reply by Igor on February 5, 2016 at 3:18pm

Hi Dana

At you it won't turn out to change a cube to a dodecahedron because the cube contains 6 faces, and a dodecahedron 12.

But the answer contains in your link https://en.wikipedia.org/wiki/Rhombic_dodecahedron#mediaviewer/File... . It is necessary to replace each edge with a face only.

You will need the Sandbox add-on/

Attachments:

• Rhombic_Dodecahedron.gh, 12 KB

Permalink Reply by mark zirinsky on February 5, 2016 at 3:35pm

If you wanted to morph from one shape to the other, looking at the animation, in that one the edges of the cube are split at the midpoints. These move in a dual opposing pair motion, either toward each other, or away from each other, to morph the cube into a pyritohedron, then into a rhombic- dodecahedron. By sequencing the amount of movement of these midpoints using a series, you should be able to get one to blend into the other.