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
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
This is an Order 1 Menger
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
2) Order 2 Menger Cube.
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.
idea taken to the next level. It is very fast once you understand the