Sphere is a tool for visualising various three dimensional symmetries. I initially wrote it in Java at the same time as my Cubie applet in order to play with lighting effects and work out how to show and control a 3d object. It was rewritten in javaScript in 2018. It may help generating ideas for new twisty puzzles, as it shows a sphere with various sets of cuts arranged symmetrically.

Controls:
Drag the sphere to rotate it.
Drag the coloured sliders left or right to change the depth of a set of cuts. If dragged all the way to the right, the cuts will no longer intersect the sphere.
Click on one of the polyhedra at the bottom right to change the symmetry type of the cuts of that colour.
Underneath the Sphere applet you can find a link which allows you to share the Sphere pattern you have created. Anyone opening the URL in that link will see the same pattern.

Here are some examples: