# Happy Moon Day!

To celebrate Moon Day — the anniversary of the first Moon landing — this year, I made a rhombic triacontahedron with colored images of the Moon on each face. I got the image of the Moon from its Wikipedia page, and made this polyhedral image using Stella 4d, a program you can try for free right here.

# The Icosahedron’s Fifth Stellation

The version above is colored per face, except for parallel faces, which have the same color. The one below is in “rainbow color mode.”

# Augmenting the Great Icosahedron With Prisms and Antiprisms

This is the great icosahedron, which is one of the Kepler-Poinsot solids.

All twenty of the faces of the great icosahedron are equilateral triangles. They interpenetrate, so they can be a little difficult to see. Here’s a still view, with one face highlighted.

If each of these twenty faces is augmented by a regular triangular antiprism (also known as the Platonic octahedron), here is the result — a variant of the Platonic icosahedron.

I also tried augmenting the great icosahedron with prisms, and this is the result — a variant of the Archimedean icosidodecahedron.

I made these images using Stella 4d: Polyhedron Navigator, which you can try for free at this website.

# A Stellated Polyhedron with Tetrahedral Symmetry

I made this using Stella 4d, which you may try as a free trial download right here.

# 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 Faceting of the Great Rhombicosidodecahedron

I made this from the Archimedean Great Rhombicosidodecahedron, using a program called Stella 4d. If you’d like to try Stella for yourself, you can do so, for free, at this website: http://www.software3.com/Stella.php.

# A Polyhedron Featuring Twelve Triacontagonal Faces

This polyhedron has 272 faces in all. I made it using Stella 4d, a program you can try for free at this website.

# A 362-Faced Polyhedron

This solid has, as faces, 12 regular pentagons, 20 regular hexagons, and 60 isosceles triangles, along with a bunch of quadrilaterals of various types. I made it using Stella 4d, which you can try for free at this website.