Sampler of 3d math prints

From 3D Printables

This picture shows a sampling of 3d math models. Match the descriptions with the pieces:

• a one-sheeted hyperboloid (regulus) showing the two families of lines which lie on it.
• a tessellated icosahedron consisting of 80 triangles printed with round-ish holes (2 sizes).
• a tight version of the borromean rings which minimizes total rope length with constant rope thickness.
• a self-intersecting sphere
• an integral surface of a path-curve system (perhaps the simplest ODE, x'=Ax with constant 4x4 matrix A, projectivized into 3D -- invented by Felix Klein and Sophus Lie in 1870).
• a woven polyhedron obtained by beginning with a quadrilateral mesh and replacing each quadrilateral with a knot crossing, then making sure the crossings fit together to make nice curves in 3D. One of the models shown here starts with the polyhedron called triacontahedron. (2)

For more pictures of these and other other models, go here.