11
$\begingroup$

On page 220 of Peter Engel's Geometric Crystallography, he describes a 38-sided convex polyhedron that can fill space.

I've seen this this accepted as the record in various places, but I've never seen a 3D picture. Has anyone ever managed to make one?

  • 0
    I've managed to see Engel's article. No coordinates there, unfortunately (but there might be useful information in there I just haven't seen). My German is no longer as great as it used to be, so if anyone wants to take a stab at constructing the polyhedron, and has good grasp of technical German, I can hook you up with a copy of Engel's article.2011-08-19

2 Answers 2

3

There is a "schematic drawing" of the Engel polyhedron in Marjorie Senechal's book Crystalline Symmetries. It appears as Figure 1.14 on page 14.

  • 0
    I'm hoping to find something suitable for looking at the 3D graphics of it, including a manipulative 3D object of an Engel38 surrounded by 38 others. I'm also hoping to do 3D printing of it at Shapeways. $G$runbaum lists coordinates for the other polyhedra, but not for this one.2011-07-07
5

Here is the figure (I assume it is this one) in Grünbaum's paper to which Joe Malkevitch refers:
      Fig. 10: Engel

  • 0
    I'm familiar with these pictures, but I'll accept them. I'd really like to get a 3D version of the packing.2011-10-03