All dimensions Wiki
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All dimensions Wiki

Best's Polytope Naming System, is a polytope naming system inspired by this other polytope naming system and names polytopes by their dimensions, and how they are folded up.

  • A cube in this polytope naming system would be called a 3D-6-2D-4-1D-Line-Fold-Fold.
  • A sphere however, would be called a 3D-Round, which is much simpler.
  • A tetrahedron would be called a 3D-4-2D-3-1D-Line-Fold-Fold.
  • A line would simply be called a 1D-Line, and a point would be called a 0D-Point.

Let's tell you the process of naming these. Once you get used to it, it's not that hard.


First, you type the number of dimensions the shape has, and then a D.

If the shape is 1D or 0D, you then just simply put "-Line" or "-Point" at the end. The line is for 1D and the point is for 0D.

If the shape is a hypersphere, you then put "-Round".

If the shape has more than 1 dimension and is not a hypersphere, you then put a dash then the amount of shapes you need to fold up into that shape, then you put another dash, then you use the system again for the shape that is folded up into the polytope, then you put another dash, then "Fold" after that dash. If you're doing the recursion process, continue to put "-Fold" at the end until the "-Fold" is linked to the first polytope you want to name in the process.


Now let's do this process on a cube.

We know that the cube is 3D, so we change the text to "3D-".

Since we know 3>1 and a cube is a fold of 6 squares, we change the text to "3D-6-".

Now we must name a square in this system. We know a square is 2D, so we change the text to "3D-6-2D-".

Since we know 2>1 and a square is a fold of 4 lines, we change the text to "3D-6-2D-4-".

Now we must name a line in this system, which is simple with one of the examples above. We just change the text to "3D-6-2D-4-1D-Line-".

We are back to 2 iterations deep of this. We now finish it off with a full text of "3D-6-2D-4-1D-Line-Fold-Fold".

There you go, you named your first polytope with this naming system.

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