Jump to content

aeh5040

Eurobricks Knights
 View Profile  See their activity

  • Posts

    791

  • Joined

  • Last visited

 Content Type 

Everything posted by aeh5040

  1. aeh5040
    That looks very interesting, but it's not quite what I meant, although perhaps it is a helpful step. I want each axle to start and end in an axle hole (as in the basic lattice), and pass through the other pin holes on the way. It's possible what you've done could achieve this (in a much sparser way than I was imagining). I think this amounts to the question: if you continue every axle beyond its stop, will it meet another stop end-on before it runs into anything else (including another axle)?
  2. aeh5040
    The offset from one unit to the next is 1/2 stud in one direction and 1 1/2 in another direction (and the third direction depends on the axle length of course). I'll see if I can make an lxf, although LDraw is my usual medium. Intertwining does sound like the right idea, but I think there may need to be more than two lattices. One thing is for sure - each axle needs to end up going through exactly 2 further pinholes. This is because the number of units is 3 times the number of axles but each unit has 6 unused holes. I tried offsetting copies in Mlcad, but it just got too confusing - I could not see war was happening nor whether things were colliding.
  3. aeh5040
    Cool. For some reason that picture especially helps clarify what is going on for me. One more little observation: you can replace half the connectors in one type of square (the big one in that last picture) with 10197 for yet another variation.
  4. aeh5040
    Cool! I can at least see why such a space filling is possible (independently of the Lego!). If you make the cuboctahedra meet at the square faces they form a cubic lattice, and the gaps between them are octahedra.
  5. aeh5040
    I have not succeeded in doing this, although I feel fairly sure it should be possible. Come on folks, help me!
  6. aeh5040
    I see, I actually had not realized that! I think you are right. In the original picture you can see another copy of the primitive nestled between the others, in multiple colors... Btw, it would be nice to see the original with all 2L axles replaced with 3L. Then all squares would be the same size. Then the question arises, can we put a connector in the middle of each of those 3Ls and connect them somehow...
  7. aeh5040
    That's right, although it also works if you replace precisely all the 2L axles between 'primitives' (the ones that are sticking out in the first picture) with 32. (This is what I meant originally). In both versions, all the edges of the resulting lattice are 'paired'. It's harder to see this for the octahedra above because of where you chose to stop... The one with all 2L axles lengthened is cool too btw! I like the way these produce 45 degree angles without using any 45 degree part, and without any approximations (like a 7-7-10 triangle). A priori I would have thought this might not be possible.
  8. aeh5040
    If I've got it right, this beauty from the "Chemistry" thread is in fact an instance of the tetrahedron-octahedron tiling of space. Replace the 2L axles with something much longer (e.g. 32L) to see the tetrahedra and octahedra...
  9. aeh5040
    Here is a quick rhomicuboctahedron:
  10. aeh5040
    It depends in part what you are willing to count as a vertex. Your "Icosahedron (truncated)" below can already be viewed as a distorted small rhombicosidodecahedron (which is the solid pictured above). However, the snub cube (and snub dodecahedron) are genuinely different. That's why I particularly mentioned that as a challenge...
  11. aeh5040
    I like it! Reminds me of a rhinoceros beetle:
  12. aeh5040
    In addition to the Platonic solids there are 13 Archimedean solids: http://en.wikipedia.org/wiki/Archimedean_solid. Can someone make a snub cube?
  13. aeh5040
    That's correct, except that the word is "dual". http://en.wikipedia.org/wiki/Dual_polyhedron Of course one can! Just use #2 connectors for the two intersecting edges, since they intersect at right angles. Didumos is right. You can see that it's impossible to tile a regular tetrahedron with regular tetrahedra by the fact that the dihedral angle, arcos(-1/3)=109.47 deg, is not a multiple of 360 deg. On the other hand, tetrahedra and octahedra together will even tile space. I used essentially the same construction (but a slightly more compact version) for the vertices of the tetrahedra in the compound of five tetrahedra. The five tetrahedra are not connected but weave through each other, and their vertices lie on the vertices of a regular dodecahedron. It was extremely difficult to assemble this (one of the hardest things I've ever made, in fact).
  14. aeh5040
    That's correct! Nicely done.
  15. aeh5040
    Wow, those are beautiful! I especially like the truncated icosahedron - I never thought I would be interested in that piece! Something I found recently that might be useful to you: the dihedral angle of a tetrahedron, arcos(1/3) = 70.5 deg, appears as an angle of certain integer triangles, which can be made with liftarms. A 2-3-3 triangle is the smallest.
  16. aeh5040
    I have a new challenge relating to this one, in the spirit of Didumos69's signature(!) Notice that the basic unit has 6 unused pin holes, one in each connector, and these holes are accessible from both sides (unlike the others). Is it possible to arrange several offset copies of the sparsified lattice (with appropriately chosen axle lengths) so that all these holes are filled (by axles from other copies going through them)? Each axle would have to go through two holes.
  17. aeh5040
    Great work! For a further challenge, try making legal instructions for this one:
  18. aeh5040
    Awesome work, folks! I particularly like this one. Interesting that it consist entirely of squares, of two different sizes.
  19. aeh5040
  20. aeh5040
  21. aeh5040
    Congratulations! I find this one quite mind boggling...
  22. aeh5040
    Is there anything along these lines that can be done with just ONE type of part, I wonder? Bionicle parts often have many holes and protrusions in multiple directions....
  23. aeh5040
  24. aeh5040
    Beautiful! What happens if you use longer axles (4L say)? Can it slide around or is it still rigid? I looked into this at the time, and I seem to remember finding that there are actually several forms of graphite, of which one was the "3 layer" type. But I agree it is certainly not the usual form. By the way, David Luders made some nice LDD versions of my "crystal": https://www.flickr.com/photos/42988571@N08/13925365761
  25. aeh5040
    Yes, it would be great to have such things. However, the fact that we don't does not mean it cannot be done with existing parts. In fact, it can - the question is how compactly and strongly. To get started, here is a way to make an exact corner of a regular tetrahedron that is both strong and compact:
×
×
  • Create New...