1polytopes(6x) XScreenSaver manual polytopes(6x)
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6 polytopes - Draws one of the six regular 4d polytopes rotating in 4d.
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9 polytopes [--display host:display.screen] [--install] [--visual visual]
10 [--window] [--root] [--window-id number] [--delay usecs] [--fps]
11 [-5-cell] [-8-cell] [-16-cell] [-24-cell] [-120-cell] [-600-cell]
12 [--wireframe] [--surface] [--transparent] [--single-color] [--depth-
13 colors] [--perspective-3d] [--orthographic-3d] [--perspective-4d]
14 [--orthographic-4d] [--speed-wx float] [--speed-wy float] [--speed-wz
15 float] [--speed-xy float] [--speed-xz float] [--speed-yz float]
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18 The polytopes program shows one of the six regular 4d polytopes
19 (5-cell, 8-cell, 16-cell, 24-cell, 120-cell, or 600-cell) rotating in
20 4d. The program projects the 4d polytope to 3d using either a perspec‐
21 tive or an orthographic projection. The projected 3d polytope can then
22 be projected to the screen either perspectively or orthographically.
23 There are three display modes for the polytope: mesh (wireframe),
24 solid, or transparent. Furthermore, the colors with which the polytope
25 is drawn can be set to either single color or to a coloring according
26 to the 4d "depth" (the w coordinate) of the polytope in its unrotated
27 position. In the first case, the polytope is drawn in red. This col‐
28 oring combined with transparency gives a nice visual effect of the
29 structure of the polytope. The second mode draws the polytope with a
30 fully saturated color wheel in which the edges or faces are colored ac‐
31 cording to their average 4d "depth". This mode is best combined with
32 the wireframe mode, where it allows you to see how different parts of
33 the polytope are moved to the "inside" of the projected polytope in 3d.
34 Of course, in 4d the cells, faces, and edges of the polytope all have
35 the same distance from the center of the polytope. Only the projection
36 creates the appearance that some of the cells lie "inside" the figure
37 in 3d.
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40 polytopes accepts the following options:
41 --window
43 Draw on a newly-created window. This is the default.
44 --root Draw on the root window.
46 --window-id number
48 Draw on the specified window.
49 --install
51 Install a private colormap for the window.
52 --visual visual
54 Specify which visual to use. Legal values are the name of a
55 visual class, or the id number (decimal or hex) of a specific
56 visual.
57 --delay microseconds
59 How much of a delay should be introduced between steps of the
60 animation. Default 25000, or 1/40th second.
61 The following six options are mutually exclusive. They determine which
63 polytope is displayed.
64 -5-cell Display the 5-cell. The 5-cell is the 4d analogon of a regular
66 tetrahedron in 3d. It has 5 regular tetrahedra as its cells,
67 10 equilateral triangles as faces, 10 edges, and 5 vertices.
68 -8-cell Display the 8-cell (a.k.a. hypercube or tessaract). The 8-cell
70 is the 4d analogon of a cube in 3d. It has 8 cubes as its
71 cells, 24 squares as faces, 32 edges, and 16 vertices.
72 -16-cell
74 Display the 16-cell. The 16-cell is the 4d analogon of an oc‐
75 tahedron in 3d. It has 16 regular tetrahedra as its cells, 32
76 equilateral triangles as faces, 24 edges, and 8 vertices.
77 -24-cell
79 Display the 24-cell. The 24-cell has no 3d analogon. It has
80 24 regular octahedra as its cells, 96 equilateral triangles as
81 faces, 96 edges, and 24 vertices.
82 -120-cell
84 Display the 120-cell. The 120-cell has no 3d analogon. It has
85 120 regular dodecahedra as its cells, 720 regular pentagons as
86 faces, 1200 edges, and 600 vertices.
87 -600-cell
89 Display the 600-cell. The 600-cell has no 3d analogon. It has
90 600 regular tetrahedra as its cells, 1200 equilateral triangles
91 as faces, 720 edges, and 120 vertices.
92 The following three options are mutually exclusive. They determine how
94 the polytope is displayed.
95 --wireframe
97 Display the polytope as a wireframe mesh.
98 --surface
100 Display the polytope as a solid object.
101 --transparent
103 Display the polytope as a transparent object (default).
104 The following two options are mutually exclusive. They determine how
106 to color the polytope.
107 --single-color
109 Display the polytope in red.
110 --depth-colors
112 Display the polytope with a fully saturated color wheel in
113 which the edges or faces are colored according to their average
114 4d "depth", i.e., the w coordinate of the polytope in its unro‐
115 tated position (default).
116 The following two options are mutually exclusive. They determine how
118 the polytope is projected from 3d to 2d (i.e., to the screen).
119 --perspective-3d
121 Project the polytope from 3d to 2d using a perspective projec‐
122 tion (default).
123 --orthographic-3d
125 Project the polytope from 3d to 2d using an orthographic pro‐
126 jection.
127 The following two options are mutually exclusive. They determine how
129 the polytope is projected from 4d to 3d.
130 --perspective-4d
132 Project the polytope from 4d to 3d using a perspective projec‐
133 tion (default).
134 --orthographic-4d
136 Project the polytope from 4d to 3d using an orthographic pro‐
137 jection.
138 The following six options determine the rotation speed of the polytope
140 around the six possible hyperplanes. The rotation speed is measured in
141 degrees per frame. The speeds should be set to relatively small val‐
142 ues, e.g., less than 4 in magnitude.
143 --speed-wx float
145 Rotation speed around the wx plane (default: 1.1).
146 --speed-wy float
148 Rotation speed around the wy plane (default: 1.3).
149 --speed-wz float
151 Rotation speed around the wz plane (default: 1.5).
152 --speed-xy float
154 Rotation speed around the xy plane (default: 1.7).
155 --speed-xz float
157 Rotation speed around the xz plane (default: 1.9).
158 --speed-yz float
160 Rotation speed around the yz plane (default: 2.1).
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163 If you run this program in standalone mode you can rotate the polytope
164 by dragging the mouse while pressing the left mouse button. This ro‐
165 tates the polytope in 3D, i.e., around the wx, wy, and wz planes. If
166 you press the shift key while dragging the mouse with the left button
167 pressed the polytope is rotated in 4D, i.e., around the xy, xz, and yz
168 planes. To examine the polytope at your leisure, it is best to set all
169 speeds to 0. Otherwise, the polytope will rotate while the left mouse
170 button is not pressed. --fps Display the current frame rate, CPU load,
171 and polygon count.
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174 DISPLAY to get the default host and display number.
175 XENVIRONMENT
177 to get the name of a resource file that overrides the global
178 resources stored in the RESOURCE_MANAGER property.
179 XSCREENSAVER_WINDOW
181 The window ID to use with --root.
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184 X(1), xscreensaver(1)
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187 Copyright © 2003-2005 by Carsten Steger. Permission to use, copy, mod‐
188 ify, distribute, and sell this software and its documentation for any
189 purpose is hereby granted without fee, provided that the above copy‐
190 right notice appear in all copies and that both that copyright notice
191 and this permission notice appear in supporting documentation. No rep‐
192 resentations are made about the suitability of this software for any
193 purpose. It is provided "as is" without express or implied warranty.
194
196 Carsten Steger <carsten@mirsanmir.org>, 28-sep-2005.
197X Version 11 6.08-1.fc39 (17-Oct-2023) polytopes(6x)