Grasshopper

algorithmic modeling for Rhino

Hi all ,

Can anyone help me to make a chain of cubes which deform to rhombic dodecahedron ?? i mean , it starts as cube and ends with rhombic dodecahedron ?

thank you

dana

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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.

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 

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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/

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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.

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