Read Me for Spin It! v1.0, a four dimensional object rotater.
Instructions:
Open (double-click on) one of the object files. What you will see is a four dimensional object inside a kind of ╥virtual trackball╙ (the blue circle).
Drag the mouse around on the trackball and see what happens. This is a rotation in the x-y-z space.
Choose other tools from the tool palette and drag around with those. Use balloon help to get a description of what these tools do.
Shortcuts: The option and command keys switch between various tools without having to select them. The cursor changes to tell you what tool you╒re using.
Use Balloon Help to get a description of what the various menu items do.
A hidden feature: When the Caps-Lock is on, the break is off.
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Miscellaneous Questions:
1) Why does the image sometimes flicker when I drag it around?
There probably isn't enough memory for Spin It! to make on offscreen copy of the window. Lower your screen depth, shrink your window, or give Spin It! more memory.
2) How do I make my own object files?
If you want to make your own objects, you will need an idea, a mathematical bent, and a resource editor or compiler. Look in the folder "Making Your Own Objects" for technical info. Don't forget to add text for the "Get Info..." window, and please send me a copy of any objects you build.
3) What is a ╥Shèfli╙ symbol? (seen in "Get Info...")
It╒s a notation that describes certain classes of regular and semi-regular geometric figures. The first number in the symbol is the number of sides in a polygon. ({3} is a triangle, {4} is a square.) The second number is the number of polygons that meet at a corner. ({3,4} is an octahedron because it has four triangles at each corner, {4,3} is a cube because it has three squares at each corner.) The third number is the number of cells (3D objects) that meet at each edge. ({4,3,3} is a hypercube because it has three cubes ({4,3}) meeting at each edge.) There are other variations on the notation. See Coxeter's Regular Polytopes for more details.
4) What is a ╥dual╙? (seen in "Get Info...")
Consider a square. If you rotate the square by 90í you get the same square back again. We say that ╥rotation by 90í╙ is a symmetry of the square. The square has other symmetries as well. The set of all symmetries of the square is called the symmetry group of the square.
Two objects are duals of each other if they have the same symmetry group. For example, a cube and an octahedron are duals. In particular, every rotation about one of the faces of the cube is equivalent to a rotation about a vertex of the octahedron, and vice versa.
If two objects are duals of each other, then their Shèfli symbols are reverses of each other. For example, a cube is {4,3} and an octahedron is {3,4}. A Hypercube is {4,3,3} and its dual is the 16-Cell {3,3,4}, what I have called a Hyper-Ocathedron. Some objects are self-dual, like the tetrahedron {3,3}, the simplex {3,3,3}, and the 24-Cell {3,4,3}.
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No warrantee expressed or implied. Bug reports are welcome.
Please tell me what you think.
James Jennings
jennings@halcyon.com
Spin It! version 1.0 and it's object files are copyright ⌐ 1995 by James Jennings. All rights reserved.
You may distribute freely for non-profit and educational use, as long as this notice is attached.
For further reading:
Regular Polytopes by H. S. M. Coxeter, ⌐1963 by Coxeter, ⌐1973 Dover Publications
Beyond the Third Dimension by Thomas F. Banchoff ⌐1990 Scientific American Library
Geometry, Relativity, and the Fourth Dimension ⌐ 1977 by Rudolf v. B. Rucker, Dover Publications
