Yesterday I mentioned a curious cardboard prop that Rudy Rucker once showed me. Van Thal emailed and said: I made one of those from his instructions in The Fourth Dimension back in the 80s, and a search this morning uncovers the instructions on this page (figure 9). It still beguiles me, and really did change the way I looked at corners forever. Not a claim that can be made by many diagrams." Link
L. Perg sez: "I've built hypercube shadows! Zometools are incredibly fun in their own right — I own an embarrassingly large amount of them. 4D cube shadows can be built with the smallest kits, however. I've linked to a very nice diagram and explanation of how to view and build hypercubes (unfortunately a .pdf) with Zometools. Of course, it is much more fun to build them.
"Zometools are also great for playing with bubbles. Zome shapes also make striking architechture that is much more flexible than domes (this what they were originally designed for). They are also great at teaching geometric and mathematic concepts. Some scientists use them also, although personally they won't do what I need — I can make a single true tetrahedron, but can't link them correctly to make silicate minerals. Also, the twist ratio in the DNA model is not correct. Overall, though, they whup any building sets that I had as a child, which is really the important thing."
Nicholas sez: I know this is going to sound crazy, but please humor me by reading
Seeing the "4D Rucker Cube" post today was quite the synchronicity. Just
yesterday I had purchased a copy of the books Hyperspace, and Surfing
Through Hyperspace. I am actually a student of Michael Bertiaux (occult
author of the Voudon Gnostic Workbook), and had read a couple of nights
ago in the Monastery of the Seven Rays first years course about the
hypercube. I had the thought that the puzzle Cube 21 (also known as the
Square 1) might possibly be a shadow of a hypercube. I have been using
this puzzle in my esoteric research. There is a shape that it can be
changed into which I call the Z(OM-B) Configuration. The middle layer is
turned 45 degrees from the top and bottom sections, which can also be
done with a normal Rubik's cube. This creates a sort of 8 pointed star.
The 8 points suggest many things, one attribution might be space-time.
This eight pointed star appears in Bertiaux's Voudon Gnostic Workbook on
a paper about occult time travel. I had the thought after reading about
the hypercube in the Monastery papers that perhaps the cuboid at the
center of the cube could be an example of a cube within a cube, or a
shadow of a hypercube. Furthermore I thought that like someone in the
fourth dimension when in this configuration we are able to see inside an
opaque 3-d object.
Another thought I had after reading the chapter on the fourth dimension
in Hyperspace is that the Lovecraftian Outer One known as Yog Sothoth
might be from this realm. He is described as being many iridescent
blobs, and is said to be the key and the gate to other dimensions. In
Hyperspace a 4-D being in our 3-D world was described as a "a blob like
creature that constantly changes shape and size." In the Dunwich Horror
Lovecraft writes that "Past, present, future, all are one in Yog-Sothoth."
Finally I had the thought that perhaps our experience of time as the
present is similar to the way that flatlanders experience the third
dimension, as shrinking and expanding cross sections. We seem to also
experience time as a cross section.
One last coincidence is the name of the company that sells the Hypercube
kits. The name Zome is very close to the name of my ZOM-B Configuration.
Here are some links to the references made above.
Here's a link to Michael Bertiaux's website.
I also wrote years ago a review of the Voudon Gnostic Workbook.
Finally about a year ago I wrote a brief paper about the Hypercube.