Spinning Dipyramids

I made these videos using my cell phone and a magnetic ball-and-stick polyhedron building system which my wife bought for me. It’s the sticks that have magnets in them, not the steel balls. First, a triangular dipyramid (n = 3). This is the simplest of the dipyramids.

Next, a square dipyramid, also known as an octahedron (n = 4).

Next, for n = 5, the pentagonal dipyramid.

If you limit yourself to dipyramids that have equilateral triangles for faces, that’s the complete set. Here’s what happens when you try n = 6 — the dipyramid has zero height, and collapses into a pair of isosceles trapezoids when lifted.

To get this to work, you’d need to use isosceles triangles, not equilateral ones. The same is true for n = 7 and greater numbers.

A Compound of Three Square Dipyramids

The reason I am not calling this a compound of three octahedra is that the faces of the dipyramids aren’t quite equilateral. They are, however, isosceles.

compound of three square dipyramids

This was created with Stella 4d, which you can buy, or try for free, right here.

More Polyhedra, Including Some Compounds, from the Stellation-Series of the Tetrakis Cube

Tetrakishexa stellation

The next one is a compound of eight off-center pyramids. By this point, I had gone so far into the stellation-series (a search I began when preparing the post before this one) that I had lost count.

compound of eight off-center pyramids

This one is a compound of three short square-based dipyramids:

compound of three short square dipyramids

This one, according to Stella 4d, is a compound of three parts, but I can’t quite figure out what the parts are!

more from the stellation series of the tetrakis cube

Here is another “mystery compound,” this one with two parts:

bizarre two-part compound

Stella 4d, which I used to make these, may be tried here.

A Pulsating Compound of Three Octangular Dipyramids


Pulsating Compound of Three Octangular Dipyramids

Software credit: see http://www.software3d.com/Stella.php for the software used (Stella 4d) to make this image. A free trial download is available.

A Compound of Three Non-Regular Square Diyramids


Compound of Three Non-Regular Square Diyramids

The only irregularity to be found here is that the faces of the dipyramids are isosceles, not equilateral.

Software credit: see this website to try the program I used to make this rotating .gif image. It’s called Stella 4d: Polyhedron Navigator.