You never need these. Everything required to solve each cache is on its cache page and in the field. Each tool runs entirely in your browser: nothing you type is sent anywhere, and it keeps working once it has loaded, even if you lose signal.
Before you start
A polytope is a flat-sided shape in any number of dimensions: a polygon in two, a polyhedron in three, a polychoron in four. Its corners are vertices, its sides are edges, and in three dimensions its flat sides are faces.
Each tool works out its facts from the shapes themselves. Each has a notepad for the facts you collect, shared between the tools in this folder and kept only in your browser.
The tools
- Interactive · 3D Nets and Folding Watch the nets of polyhedra fold up in 3D; draw your own net on a square or triangle grid to see whether it folds into a cube or another solid and which faces end up opposite; and flex a trihexaflexagon or hexahexaflexagon, with your own labels, to see which face turns up next.
- Interactive · 4D Polychora The four-dimensional polytopes: the six regular convex ones, the ten regular star ones, the snub 24-cell and the grand antiprism. Turn them through the fourth dimension, look up their cells, counts, densities, symmetry and sizes, and filter by facts to find the one that fits a clue.
- Interactive · 2D Polygons Regular polygons, star polygons and their compounds. Draw them with their diagonals, look up names, angles and sizes at any scale, count diagonals and their crossings, and find the polygon that fits one known fact.
- Interactive · 3D Polyhedra Every uniform polyhedron, star ones included, plus the Catalan solids, prisms and antiprisms. Turn them in 3D, look up counts, angles, symmetry, names and numbers, and filter by facts to find the shape that fits a clue.