Content about “

editorial

”

The Venus torso is a highly complex shape to unfold. Surprisingly there exists an unfolding consisting of a single component.

The world's most important solid. The soccer ball has positive curvature at each vertex

Unfolding a non-convex shape such as this horse model requires an intensive numerical search.

Dodecahedron with a different unfolding

An unfolding of a cube

The Császár torus is an embedded polyhedral torus (i.e. one without self-intersection) with the least number of vertices

The Clifford torus is generated by a family of circles which unfolds nicely despite the negative curvature of the inner region

The catenoid is a minimal surface with "too much" negative curvature. Therefore, the unfolding consists of more than one planar component.

The discrete Boy surface unfolds to a simply connected disk. Opposite vertices of the boundary are identified during refolding

A planar unfolding of the Boy Surface

Original drawing of the cutting lines of the paper model of the Boy Surface