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(Drag on screen to change rotation.) There are 5 regular polyhedra: tetrahedron (4 triangular faces); cube (6 square faces); octahedron (8 triangular faces); dodecahedron (12 pentagonal faces); icosahedron (20 triangular faces). In each case if one puts a point in the middle of all the faces and and joins those points up with their nearest neighbors a new polyhedron is formed, also regular, the dual of the one we started with. The tetrahedron is its own dual; the cube is dual to the octohedron; and the dodecahedron is dual to the icosahedron. These latter two instances are illustrated in this interactive animation. I put it together to see what could be in done Flash 5 to simulate 3-D. |