Many of the constructions are animated by the # slider, or the $ slider, or both.
Nets (12 July 10) contains nets for all eighteen Platonic and Archimedean polyhedra.
Samples (12 July 10) contains several diverse demonstrations, as follows:
The rhombic dodecahedron tiles 3-space, as suggested by rhdodecalatt.
120cell is a two-dimensional picture of a three-dimensional projection of a famous four-dimensional polytope. Move the # slider to take a Hamiltonian tour of all 120 dodecahedra.
fivecubes is a compound of five cubes, using the vertices of a regular dodecahedron.
fiveoctahedra is a compound of five octahedra, using the vertices of the Archimedean icosidodecahedron.
fivetetrahedra is a compound of five tetrahedra, using the vertices of a regular dodecahedron.
octahedron2 dissects an octahedron into tetrahedra and smaller octahedra.
tetrahedron2 dissects a tetrahedron into an octahedron and smaller tetrahedra.
binomcube shows a 27-piece dissection of a cube that is based on the expansion of (m+1)^3.
A famous result of Archimedes states that the volume of a cylinder equals the combined volume of an inscribed cone and an inscribed sphere.
The Pythagorean Theorem is illustrated by pythag1, pythag2, and pythag1.
Henry Dudeney devised a famous simultaneous dissection of a square and an equilateral triangle, illustrated by sqtr1 and sqtr2.
How many cubes do you see in cubes? This is a familiar optical illusion produced by drawing a couple of hexagons and doing some coloring.
The unit-circle definition of sine and cosine comes to life in circfns.
parab is a dynamic tangent-line construction for parabola. Drag either the focus or the bulleted point on the directrix. If you drag the focus, you should first enable Anim|Monitor Tracing, so that the parabolic tracing will be updated as you go.
parabola is like the preceding, except that the # slider controls the point on the directrix.
parabenv is like the preceding, except that the tracing shows an envelope of tangent lines.
Any quadrilateral can be used as a tile, as illustrated by checkers. Drag the bulleted points (gently) to alter the fundamental region.