What is the name of this geometric figure?

Link to the least-lousy picture I could find of an example: http://www.steelpillow.com/polyhedra/icosa/tidystelfacet/sphere_cells.png
Only with each two parallel bands in the example replaced by single line.

It’s related to the icosahedron obviously and it’s symmetrical, but it’s not a semi-regular polyhedron since neither the triangles nor the hexagons are regular. I think it’s what you get when you take a truncated icosahedron (soccerball pattern) and then truncate it again. It may not be obvious from the picture, but it’s edges form ten great circles each dividing a sphere in half, and so it could be considered a family with the octahedron, cuboctahedron, and icosidodecahedron, which do the same thing with three, four, and six great circles. In fact they could be considered corresponding to the four Platonic solids that have three, four, six and ten opposing vertices and faces.

Anyway, as this long-winded explanation shows, it would really help if I could knew this beast’s name.

A dodecahedron?

Ball of yarn?

It’s a tricky one; I agree that it might be a twice-truncated icosahedron, but I’m having a little trouble visualising it from the picture provided. Afraid I’ve got to run off so can’t chase this down more, but there’s a rather magnificent Encyclopedia Polyhedra that might be of use to you; it has a whole bunch of VRML 3D models to view if you’ve got the right browser plugin. Hope this helps…

This appears to be correct. I don’t know if there’s a standard name for that, though.

“Truncated truncated icosahedron” seems to be the most common term I’ve seen while meandering around some geometric origami and math websites.

Searching that site found the image used near the bottom of this page. The caption there is “Sphere intersecting the infinite cells of the stellated icosahedron”.


On second thought…

Wonderful site DB! The closest I found was quasi-regular polyhedra, which my figure doesn’t quite meet the technical defintion of, but shares the property of the edges forming great circles. It’s similar in appearance to the dodecadodecahedron, except it’s convex.

reviving this thread because I have something new to add- a better picture of what I was trying to describe:

A dodecadodecahedron.

Here’s a list of all kinds of uniform polyhedra, too.

Image search for Triaxial Sphere leads to several examples of what I was talking about.

Irregular pentagon.

irregular is perhaps due to error in the lines - it could be a regular pentagon if the lines that formed the sides were accurate.

A pentagon is a two-dimensional figure. This is three-dimensional.

According to the Balcones Forge newsletter from April 2008 (warning: PDF), it’s an Icosidodecahedron. We made one out of 5 strips of steel. There are some pictures if you care to download it.


Close but no cigar. An Icosidodecahedron requires six bands; the figure this thread is about requires ten.

In France they call it a boule. :slight_smile:

In Hogwarts they call that a snitch.

But seriously, looking at the OP’s example, it looks like a spherical dodecadodecahedron, which legend holds can only be destroyed in the very fires that forged it.