OK, just in case this kind of surface has no name yet and just in case I have naming rights, I hereby dub it a "pringle".* —Dan P.S. No, they're not caltrops. You can't eat them. _________________________________________________________________________ * Consistent with the edibility of the other shape-name I came up with, the "bialy" — created by rotating a vertical circle tangent to the z-axis about the z-axis.
On Oct 13, 2015, at 11:07 AM, James Buddenhagen <jbuddenh@gmail.com> wrote:
Dan's second description allowed me to draw it by hand. Here is another way to describe it:
Start with a regular tetrahedron. (It doesn't have to be regular, but that makes it easier to visualize.) Rest that on an edge say on table top, with opposite edge above the table also horizontal. Now take the midpoint of the top edge E' and draw the lines to the bottom vertices, subdividing two of the tetrahedral faces each into 2 right triangles. Similarly, take the midpoint of the bottom edge F' and join it to the two top vertices, thereby subdividing the other two tetrahedral faces each into 2 right triangles.
Now deform this tetrahedron (which now is 8 right triangles, 4 pairs of co-planar right triangles), by moving points E' and F' toward each other, making an non-convex octahedron, with the 8 right triangles each deformed (they can still be congruent) so they are obtuse. That is the object.
Seems like it must have a name, but I don't know one.