> 4D Blocks
> Version 6
Kinds of Blocks
More Geometry Examples
Geometry Examples #3
Elevated Train Examples
Round Platform Examples
Toys and Puzzles
Shape ReferenceThis is reference material, but it can be fun to look at. For every shape X defined in the library files in the "lib" directory, there's a corresponding "single-X" file in the "single" directory that displays just that one shape. The shapes are in their default positions and orientations except that I've lifted a few of them up so that they're not stuck in the ground. I'm going to comment on all the shapes, so if there's a particular one you're interested in, just scroll down and look for the name in bold.
In Geometry Examples I used a standard set of blocks to build arches and spheres and so forth, and then later at the end of More Geometry Examples I introduced a compact set of blocks that could be used to do the same things. Here's a nice table from the latter that shows how the pieces correspond.
block3 diag3 ceil3
The first few shapes are all completely straightforward.
The remaining shapes need a bit more explanation.
These last two shapes aren't in the table, but I think they count as building blocks anyway.
These four basic shapes don't appear anywhere except here.
Although those four shapes don't appear anywhere except here, two of them do show up in different orientations.
Here are two more basic shapes.
The following shapes are all discussed at length in Geometry Examples #3.
This last shape is discussed at length in Contributed Examples.
In case it helps, here's a table of all the regular polyhedra and polychora.
Fun Geometry Facts
If you think of the vertices and edges of a cube as forming a graph, that graph can be colored with just two colors. If you take the vertices of one color and make a shape out of them, you get an inscribed tetrahedron. The same construction in 4D gives you an inscribed hexadecachoron. There were two colors, so there are two inscribed tetrahedra and two inscribed hexadecachora. However, if you make a shape out of the face centers of a tesseract, you get … another hexadecachoron! And if you make that hexadecachoron exactly twice as large, then it's the same size as the other two, because 22 is equal to 12+12+12+12. Each hexadecachoron has eight vertices. If you make a shape out of all three sets of eight at once, you get … a 24-cell! It can't be colored with two colors, but because it's made of vertices from three hexadecachora and is self-dual, it can be colored with three colors in a nice symmetrical way.