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.