Enveloping the Oloid
Enveloping the Oloid
The oloid is the convex hull of two unit circles that lie in perpendicular planes where each circle contains the center of the other; you can show these circles. This Demonstration visualizes how the oloid develops from the inversion of a rectangular kaleidocycle, the center part of the evertible cube from Paul Schatz. The red line connects two vertices of the tetrahedra that form the kaleidocycle. This line is always tangent to the surface of the oloid, so when the line is moved by inverting the kaleidocycle it envelops the oloid. Some of the tetrahedra are hidden by the oloid; to make them visible, decrease the opacity of the oloid.