polytopes(6) XScreenSaver manual polytopes(6) NAME polytopes - Draws one of the six regular 4d polytopes rotating in 4d. SYNOPSIS polytopes [--display host:display.screen] [--install] [--visual visual] [--window] [--root] [--window-id number] [--delay usecs] [--fps] [-5-cell] [-8-cell] [-16-cell] [-24-cell] [-120-cell] [-600-cell] [--wireframe] [--surface] [--transparent] [--single-color] [--depth-colors] [--perspec- tive-3d] [--orthographic-3d] [--perspective-4d] [--orthographic-4d] [--speed-wx float] [--speed-wy float] [--speed-wz float] [--speed-xy float] [--speed-xz float] [--speed-yz float] DESCRIPTION The polytopes program shows one of the six regular 4d polytopes (5-cell, 8-cell, 16-cell, 24-cell, 120-cell, or 600-cell) rotating in 4d. The pro- gram projects the 4d polytope to 3d using either a perspective or an ortho- graphic projection. The projected 3d polytope can then be projected to the screen either perspectively or orthographically. There are three display modes for the polytope: mesh (wireframe), solid, or transparent. Further- more, the colors with which the polytope is drawn can be set to either sin- gle color or to a coloring according to the 4d "depth" (the w coordinate) of the polytope in its unrotated position. In the first case, the polytope is drawn in red. This coloring combined with transparency gives a nice vi- sual effect of the structure of the polytope. The second mode draws the polytope with a fully saturated color wheel in which the edges or faces are colored according to their average 4d "depth". This mode is best combined with the wireframe mode, where it allows you to see how different parts of the polytope are moved to the "inside" of the projected polytope in 3d. Of course, in 4d the cells, faces, and edges of the polytope all have the same distance from the center of the polytope. Only the projection creates the appearance that some of the cells lie "inside" the figure in 3d. OPTIONS polytopes accepts the following options: --window Draw on a newly-created window. This is the default. --root Draw on the root window. --window-id number Draw on the specified window. --install Install a private colormap for the window. --visual visual Specify which visual to use. Legal values are the name of a visual class, or the id number (decimal or hex) of a specific visual. --delay microseconds How much of a delay should be introduced between steps of the ani- mation. Default 25000, or 1/40th second. The following six options are mutually exclusive. They determine which polytope is displayed. -5-cell Display the 5-cell. The 5-cell is the 4d analogon of a regular tetrahedron in 3d. It has 5 regular tetrahedra as its cells, 10 equilateral triangles as faces, 10 edges, and 5 vertices. -8-cell Display the 8-cell (a.k.a. hypercube or tessaract). The 8-cell is the 4d analogon of a cube in 3d. It has 8 cubes as its cells, 24 squares as faces, 32 edges, and 16 vertices. -16-cell Display the 16-cell. The 16-cell is the 4d analogon of an octahe- dron in 3d. It has 16 regular tetrahedra as its cells, 32 equilat- eral triangles as faces, 24 edges, and 8 vertices. -24-cell Display the 24-cell. The 24-cell has no 3d analogon. It has 24 regular octahedra as its cells, 96 equilateral triangles as faces, 96 edges, and 24 vertices. -120-cell Display the 120-cell. The 120-cell has no 3d analogon. It has 120 regular dodecahedra as its cells, 720 regular pentagons as faces, 1200 edges, and 600 vertices. -600-cell Display the 600-cell. The 600-cell has no 3d analogon. It has 600 regular tetrahedra as its cells, 1200 equilateral triangles as faces, 720 edges, and 120 vertices. The following three options are mutually exclusive. They determine how the polytope is displayed. --wireframe Display the polytope as a wireframe mesh. --surface Display the polytope as a solid object. --transparent Display the polytope as a transparent object (default). The following two options are mutually exclusive. They determine how to color the polytope. --single-color Display the polytope in red. --depth-colors Display the polytope with a fully saturated color wheel in which the edges or faces are colored according to their average 4d "depth", i.e., the w coordinate of the polytope in its unrotated position (default). The following two options are mutually exclusive. They determine how the polytope is projected from 3d to 2d (i.e., to the screen). --perspective-3d Project the polytope from 3d to 2d using a perspective projection (default). --orthographic-3d Project the polytope from 3d to 2d using an orthographic projec- tion. The following two options are mutually exclusive. They determine how the polytope is projected from 4d to 3d. --perspective-4d Project the polytope from 4d to 3d using a perspective projection (default). --orthographic-4d Project the polytope from 4d to 3d using an orthographic projec- tion. The following six options determine the rotation speed of the polytope around the six possible hyperplanes. The rotation speed is measured in de- grees per frame. The speeds should be set to relatively small values, e.g., less than 4 in magnitude. --speed-wx float Rotation speed around the wx plane (default: 1.1). --speed-wy float Rotation speed around the wy plane (default: 1.3). --speed-wz float Rotation speed around the wz plane (default: 1.5). --speed-xy float Rotation speed around the xy plane (default: 1.7). --speed-xz float Rotation speed around the xz plane (default: 1.9). --speed-yz float Rotation speed around the yz plane (default: 2.1). INTERACTION If you run this program in standalone mode you can rotate the polytope by dragging the mouse while pressing the left mouse button. This rotates the polytope in 3D, i.e., around the wx, wy, and wz planes. If you press the shift key while dragging the mouse with the left button pressed the poly- tope is rotated in 4D, i.e., around the xy, xz, and yz planes. To examine the polytope at your leisure, it is best to set all speeds to 0. Other- wise, the polytope will rotate while the left mouse button is not pressed. --fps Display the current frame rate, CPU load, and polygon count. ENVIRONMENT DISPLAY to get the default host and display number. XENVIRONMENT to get the name of a resource file that overrides the global re- sources stored in the RESOURCE_MANAGER property. XSCREENSAVER_WINDOW The window ID to use with --root. SEE ALSO X(1), xscreensaver(1) COPYRIGHT Copyright (C) 2003-2005 by Carsten Steger. Permission to use, copy, mod- ify, distribute, and sell this software and its documentation for any pur- pose is hereby granted without fee, provided that the above copyright no- tice appear in all copies and that both that copyright notice and this per- mission notice appear in supporting documentation. No representations are made about the suitability of this software for any purpose. It is pro- vided "as is" without express or implied warranty. AUTHOR Carsten Steger <carsten@mirsanmir.org>, 28-sep-2005. X Version 11 6.15 (30-Mar-2026) polytopes(6)
NAME | SYNOPSIS | DESCRIPTION | OPTIONS | INTERACTION | ENVIRONMENT | SEE ALSO | COPYRIGHT | AUTHOR
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