Objects in my house with icosahedral symmetry

Somehow toys just show up in this house, a phenomenon which I think is familiar to many parents. Some of them have icosahedral symmetry. Like this one.

Hard plastic icosahedron ball, with stars for vertices.

You can see that the designer was outlining the vertex of an icosahedron with that five-pointed star shape, but they couldn’t quite commit – the star points don’t actually point to the next vertex! (And no, they don’t turn.) You can get a better sense of the stars corresponding to the vertices of an icosahedron here:

There’s also this one, which is softer and has a couple of distinguished vertices antipodal to each other:

Soft icosahedron, with rattly bits at two antipodal vertices.

And this one which I bought for myself years ago, presumably in some sort of store that sold housewares. (Remember stores?)

Skeleton of an icosahedron.

The nice thing about this one is that you can see through it, which makes for some interesting photographic possibilities, such as this view where two antipodal vertices are aligned:

Skeleton of an icosahedron, photographed down an axis through two vertices.

and this view with that emphasizes a threefold rotational symmetry:

Skeleton of an icosahedron, emphasizing threefold symmetry.

Of course we have a soccer ball somewhere. You know what a soccer ball looks like, I’m not taking a picture.

Finally, the Twitter feed for this blog has as its icon an icosahedron, which I got from Wikimedia Commons:

I also use this as an avatar in various work systems that need one – these generally require small pictures and a face wouldn’t show up well, and it’s easier to pick out than the default in a lot of these systems which is just someone’s initials in a circle.

I do not yet have an icosahedron as a tattoo, but I’ve liked it for a while. If I were to get a tattoo it would be either an icosahedron or the diagram from Byrne’s rendition of Euclid’s proof of the Pythagorean theorem. (The link goes to Nicolas Rougeux’s interactive enhancement of the same.)

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