Curious about the space between the planets, he hypothesized that each gap must correspond to one of the Platonic solids: the tetrahedron, cube, octahedron, icosahedron, and dodecahedron.

出于对行星之间空间的好奇，他假设每间隙都必须对应拉图立体：四面体、立方体、八面体、二十面体和十二面体。

And what popped out was a perfect dodecahedron, only 11 nanometers across.

而出现的则是完美的十二面体，直径仅有11纳米。

This in its turn was placed inside an icosahedron, then followed the orbit of Earth, a dodecahedron, Mars, a tetrahedron, Jupiter, a cube, and finally Saturn.

这之后放置在二十面体内，接着是地球的轨道， 十二面体，火星，四面体， 木星，立方体，最后是土星。

Each of them is this kind of squished cube shape, and the four of them together fit very nicely to create this rhombic dodecahedron.

它们每都是这的立方体形状，并且它们四非常完美地贴合在起， 形成了这菱形十二面体。

The significance was that  that constant didn't depend on the shape itself, it could have been a square, or a cat, or the  pentagonal faces of our dodecahedron, whatever.

重要的是那常数不依赖于形状本身，它可以是正方形， 也可以是猫，还可以是我们十二面体的五边形面，无论什么形状都行。

There's a really nice video with Matt Parker and Adam Savage featuring a rhombic dodecahedron, where they construct this beautiful lightbox that features the fact that you can tessellate 3-dimensional space using this shape.

有非常棒的视频， 马特·帕克和亚当·萨维奇在视频中展示了菱形十二面体，他们用这形状构建了美丽的灯箱， 展示了你可以使用这形状来填充三维空间。

It's this very beautiful and symmetric shape, and if instead of the wire frame I make it solid, this has a special name, it's called a rhombic dodecahedron.

这是非常美丽且对称的形状，如果我把这空心框架做成实心的，它有特别的名字， 叫做菱形十二面体。

You say, imagine this has a side length of one, and you're going to use many copies of this shape to tile a big rhombic dodecahedron with some kind of integer side length.

你说， 假设这形状的边长为，你将使用许多这样的形状来铺满边长为整数的大型菱形十二面体。

The game is that every time inside this big tiling you find a small 1x1x1 rhombic dodecahedron, you make this move where each piece can slide through the middle.

游戏规则是每次在大拼接中找到边长为1x1x1的菱形十二面体时，你可以进行这样的操作：每部分都可以从中间滑动。