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

而出现的则是一个完美的十二面体，直径仅有11纳米。

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.

出于对行星的好奇，他假设个隙都必须对应一个柏拉图立体：四面体、立方体、八面体、二十面体和十二面体。

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

它们一个都是这种压扁的立方体形状，并且它们四个非常完美地贴合在一起， 形成了这种菱形十二面体。

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.

这后在一个二十面体内，接着是地球的轨道， 一个十二面体，火星，一个四面体， 木星，一个立方体，最后是土星。

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.

这是一个非常美丽且对称的形状，如果我把这个心框架做成实心的，它有一个特别的名字， 叫做菱形十二面体。

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.

重要的是那个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.

有一个非常棒的视频， 马特·帕克和亚当·萨维奇在视频中展示了一个菱形十二面体，他们用这个形状构建了一个美丽的灯箱， 展示了你可以使用这种形状来填充三维。

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.

游戏规则是次在大拼接中找到一个边长为1x1x1的菱形十二面体时，你可以进行这样的操作：个部分都可以从中滑动。

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， 假设这个形状的边长为一，你将使用许多这样的形状来铺满一个边长为整数的大型菱形十二面体。