Thread: "4D Playground"

Hi,

Yesterday when I walked through a playground, this climbing structure immed=
iately caught my eye:

http://picasaweb.google.com/lh/photo/ECkcXJX1nNniYHaRKxmbU313y-k7SArfvCdqrm=
7thV4

It really looks like a projection of a 4D polychoron! It's not one of the s=
ix regular ones but some truncated polychoron. With my wife by my side and =
some kids on it, I started examining the structure. At the center there's a=
truncated octahedron, surrounded by several (should be eight) truncated oc=
tahedra, just as in the space-filling tessellation /wiki/Bitruncated_cubic_honeycomb>. I was a little bit disappointed because=
that means not all cells are transitive. But it could still be something l=
ike a prism. I don't remember the structure of the outskirts.=20

I don't know what the designer was planning to build, but I really like thi=
s structure. I may go there another day and take a closer look, and, climb =
it. How does it feel to walk into a 4D structure (actually on the surface o=
f it)? I really want to find it out. If there's a 120-cell playground climb=
ing structure, it would really worth a trip to go into it.

Nan

Hello Nan,

It's difficult to tell from the photo. If you can go back and take two
pictures separated by two or three inches side-to-side I can put them
into a proper stereogram and probably be able to see exactly what's
going on.

I have seen similar play structures based on truncated octahedron/cube
packing, but I'd like to see the rest. My guess is that they started
with that familiar packing and the rest is just whatever it took to
anchor it well, but it will be good to know because that would
definitely be exciting to see a proper projection of one of our 4D friends.

Thanks for sharing this,
-Melinda

On 5/29/2011 1:42 PM, schuma wrote:
> Hi,
>
> Yesterday when I walked through a playground, this climbing structure immediately caught my eye:
>
> http://picasaweb.google.com/lh/photo/ECkcXJX1nNniYHaRKxmbU313y-k7SArfvCdqrm7thV4
>
> It really looks like a projection of a 4D polychoron! It's not one of the six regular ones but some truncated polychoron. With my wife by my side and some kids on it, I started examining the structure. At the center there's a truncated octahedron, surrounded by several (should be eight) truncated octahedra, just as in the space-filling tessellation. I was a little bit disappointed because that means not all cells are transitive. But it could still be something like a prism. I don't remember the structure of the outskirts.
>
> I don't know what the designer was planning to build, but I really like this structure. I may go there another day and take a closer look, and, climb it. How does it feel to walk into a 4D structure (actually on the surface of it)? I really want to find it out. If there's a 120-cell playground climbing structure, it would really worth a trip to go into it.
>
> Nan