### Meissner Tetrahedra

Printed in WSF, then dyed with fabric dye.
Printed in WSF, then dyed with fabric dye.
Showing openings in bottom
Check out gibell's Reuleaux solids at http://www.shapeways.com/model/115463/reuleaux_solids_3cm.html Those are surfaces of rotation based on Reuleaux polygons, which are curves of constant width. These are also surfaces of constant width, but *not* surfaces of rotation. So despite looking decidedly non-spherical, they roll smoothly as spheres.

There are two different Meissner solids, subtly different.  Look closely at the edges.  Some are rounded and some are sharp.  One of them has the round edges making a a triangle and the sharp edges meeting at a point; the other has them the other way around.

These are sized for compatibility with gibell's solids, so if you get all five they will all roll smoothly under the same flat surface together.  And like gibell's, they are hollow with internal braces to lend extra support, with holes in the bottom to let the support material out.

Printed great.  Video below! (the two foreground shapes are mine; the red one in the background is one of gibell's from the set linked above)

##### Tags:
Art, Mathematical Art
cm: 3 w x 2.998 d x 6.4 h
in: 1.181 w x 1.18 d x 2.52 h

@clsn Thanks a lot, I had found some links about this but most of the time they're about a sentence long without much explanation so thanks for clarifying it for me. (And of course it's only with 3 of the sides; either subtending to a point or the 3 sides of one triangular plane on the tetrahedron). Thanks again.
@G_GR3G_G , @ekul1018 Take a look at http://www.swisseduc.ch/mathematik/geometrie/bodiesofconstantwidth/docs/meissner_en.pdf for an explanation of how the rounding-off happens. Basically, you extend the planes of the base tetrahedron, remove the solid between the extensions, and complete it again with a rotation of the lines of intersection.