CSE 325 -- Computers and Sculpture
George Hart

Using Great Stella to Join Polyhedral Blocks

As seen in class, the Great Stella program has a large library of polyhedra and can do various kinds of manipulations on them. For this exercise, we start with simple polyhedra and join them face-to-face to make larger forms. The faces can be unfolded into a net and printed out to be assembled from paper (or plates of steel or whatever).

See the Help file for basic manipulations. For this exercise, you need to understand platonic polyhedra, selecting faces, storing polyhedra in memories, the Augment operation, mirror image reflection, and nonuniform scaling. Be sure you understand how the Augment operation matches the selected faces and that you can rotate with the arrow keys before accepting it. We discovered that the program sometimes crashes if you do these exercises with more than one sub-window open, so type Ctrl-1, which will close all but one sub-window. That is the digit 1.  Later you can do Ctrl-2 or Ctrl-3 to reopen 2 or 3 sub-windows.


1) 3x3x3 cube minus three central tunnels. This is an Order 1 Menger Cube. Put a cube in memory 1. Use it as a building block and arrange 20 cubes as in this figure. A fast way is to first make a ring of 8, select a corner face, and save it in Memory 2, then add four cubes to the corners and and pop on the remaining 8 as a group. Make sure you understand the various options to the Augment command and how the arrow key rotates the group being added.


2) Order 2 Menger Cube. Take the above unit, select a corner square and put it in memory. Use it as the module in making a larger cube.


3) Order 3 Menger Cube. Same idea taken to the next level. It is very fast once you understand the user interface.

 
4) Tony Smith's Moondog. A side view and top view are shown. Use the nonuniform scaling menu item to stretch a regular octahedron to twice its length along a 3-fold axis. That is the yellow connecting strut above. The red faces are the faces you can see of regular tetrahedra. This structure is part of the diamond crystal lattice, with red representing carbon atoms and yellow representing the carbon-carbon bonds. With these struts, it is amazing how it looks tilted in different directions as you walk around it. For extra credit, look up Tony Smith's sculpture Smoke, which is similar with more units, and make a model of it.

 
5) 4x4x4 lattice of snub cubes. Two views are shown above. This is an exercise in parity. You can use a doubling algorithm to make this fast and easy. Find the snub cube in the Archimedean solids. Note that it is chiral, i.e., it has left-hand and a right-hand mirror image forms. Save one of each in memories. In the above structure they connect with cubes for struts. Note that neighboring units are of the opposite handedness, i.e., a left-handed one is surrpunded by six right-handed ones. (In the infinite extension of this structure, every vertex is identical, with two squares and four equilateral triangles, i.e., it is an infinite uniform polyhedron.)

 

6) Star made of Dodecahedra.  This is easy if you use the fact that Great Sella understands the symmetry and can augment to all equivalent faces. Start with a dodecahedron. Surround all faces with a chain of four more dodecahedra. At the tip of each chain, branch out five ways with with another chain of four. Put a dodecahedron where these meet in pairs. Then add two more chains to each tip, which meet in groups of threes.Then a final dodecahedron goes at each tip. Note that the struts (chains) can be any even length.

7) Something Original. Using similar techniques, but perhaps different building blocks, create something original of your own design that is interesting, but not too complex. Next week you will print out its net, cut it out from paper, fold, tape, and assemble it.

Show the TA images of your constructions. You can be checked off at the start or end of class, or email images (taken from a different viewpoint) as attachments. Do not email the Great Stela files, as they can be large.) Have your Great Stella file that answers #7 saved somewhere where you can access it in class to show everyone.

Questions 1-6 are due tuesday Feb 17th.  Question 7 is due in class thursday Feb 19.