Help with some Space Math (sorta)

[Fred Brackin]

Originally Posted by Varyon

EDIT: . Indeed, it looks like you could basically stack tetrahedrons indefinitely, ..

That's how diamonds work. They're made up of many, many tetrahedrons.

[RogerBW]

Originally Posted by Varyon

EDIT: Looking at that 3d model you linked, it would appear you could place a single "double tetrahedron" (a tetrahedron with another tetrahedron growing out of one face) between each outer tetrahedron, adding an additional star. Indeed, it looks like you could basically stack tetrahedrons indefinitely, and I suspect this will be the model I'll go with just as soon as I find a good way to visualize it...

Um, you can't tesselate regular tetrahedra. Try it with d4s between thumb and finger: you can fit in five with the same two points in common, but not six.

[Anthony]

Originally Posted by RogerBW

Um, you can't tesselate regular tetrahedra. Try it with d4s between thumb and finger: you can fit in five with the same two points in common, but not six.

If you stack spheres in a hexagonal packing, and then draw lines between the centers of each sphere, those lines form tetrahedrons.

[RogerBW]

Originally Posted by Anthony

If you stack spheres in a hexagonal packing, and then draw lines between the centers of each sphere, those lines form tetrahedrons.

Oh, sure, as long as you don't mind having gaps between your tetrahedra, go wild.

(Again, you can demonstrate this with d4s. Put six into a hexagon shape. You can put three on top, same way up, balanced with corners on the top points. But there are gaps.)