Tag Archives: geometry

Business Card Archimedean Solids

are a fun way to use up the excessive quantities of old business cards that my friends give me (which, of course, they are giving me because of my propensity to fold them into things – a most excellent cycle).

I was most recently given a box of “AMA Capital” business cards and attempted to make as many of the Archimedean solids as possible from them. Several of these can be seen in the photo of my exhibit at EBOC.

I already knew how to make cuboctahedra and icosidodecahedra, as seen here, but I didn’t know how to make any of the other Archimedean solids.

Thus far, I have come up with modules and designs for the truncated tetrahedron, truncated cube, truncated cuboctahedron, rhombicuboctahedron, truncated icosahedron, and rhombicosidodecahedron. I wouldn’t be surprised if some (or even all) of these designs were examples of parallel invention, but I haven’t seen any of them elsewhere as yet, and I certainly had a fun time coming up with and building them, which is probably the important part.

Things with icosahedral symmetry

often have “small friends” with octahedral symmetry.

Seeing Stars

Icosahedral and octahedral versions of ‘Seeing Stars’

Here are the “small friends” for Seeing Stars and the chocolate wrapper sculpture that I posted earlier. Super cute, although I must admit that I like icosahedral symmetry a bit better in general (perhaps why the other sculptures were made first ^^)

Origami Conventions

are great motivators for finally finishing those models that you haven’t gotten around to. The East Bay Origami Convention¬†was this past weekend, and in addition to teaching my circus elephant, I also had a display with this model that I finally finished the night before the convention.


I’ve had this one floating around in my head ever since I saw George Hart’s Frabjous. It’s made out of 30 identical pieces intertwined as in Frabjous, although the exact shape of the pieces is a bit different, leading to a fairly distinctive end result.

One way of understanding the underlying geometry is to think of each piece as a subset of a rhombic side of the great rhombic triacontahedron, with the subset chosen such that the pieces don’t intersect.

Another strategy for understanding the model is to think of each piece as representing a line connecting opposite vertices of two adjacent pentagons in a dodecahedron. The pieces are then necessarily curved so as to avoid intersecting with each other.
The first strategy is easier if one wishes to design similar pieces. The second is easier to visualize and understand intuitively when looking at the model.

Geometric art

Shows up all over the place.
Pentagonal Hexecontahedron Lamp

Pentagonal Hexecontahedron Lamp

Even when you aren’t looking for it.
The first couple of photos are of a neat lamp at a restaurant that I went to recently. It is made out of sixty identical pieces that form a pentagonal hexecontahedral shape. The other two pieces are examples of large outdoor sculptures at MIT.

Seeing Stars

is a geometric sculpture wherein one can see many stars — made out of a material itself intended for seeing stars (or at least the sun!).


Novelty sunglasses in six different colors interlock without glue or adhesives to create these intricate, chiral sculptures. Although the individual pairs of glasses are closed in the normal manner, their interlacing enables them to maintain distinctive forms.

The sculpture is made from 60 pairs of sunglasses. It is symmetrically colored such that the edges around the structure are accentuated.