The
Reuleaux tetrahedron can be modified into a 'solid of constant width'
by replacing all six edges with sections of an 'envelope of spheres' 
a spheresweep in ray tracing terminology. The resulting solid is
spheroform and has tetrahedral symmetry.


The
sphere envelopes extend between vertices on each edge of the unit
tetradedron (edge length 1). The radius of each sphere in the envelope
is given by the function:

Each
sphere is tangent to the straight edge of an internal regular
tetrhadron, and tangent to the surface of the Reuleaux tetrahedron.



Rendered Sphere Sweep
Side view
Top view
Length view






Rendered Spheroform Tetrahedra

More Information
and Proof



