1polytopes(6x) XScreenSaver manual polytopes(6x)
2
6 polytopes - Draws one of the six regular 4d polytopes rotating in 4d.
7
9 polytopes [-display host:display.screen] [-install] [-visual visual]
10 [-window] [-root] [-delay usecs] [-fps] [-5-cell] [-8-cell] [-16-cell]
11 [-24-cell] [-120-cell] [-600-cell] [-wireframe] [-surface] [-transpar‐
12 ent] [-single-color] [-depth-colors] [-perspective-3d] [-ortho‐
13 graphic-3d] [-perspective-4d] [-orthographic-4d] [-speed-wx float]
14 [-speed-wy float] [-speed-wz float] [-speed-xy float] [-speed-xz float]
15 [-speed-yz float]
16
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
31 accoring 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.
38
40 polytopes accepts the following options:
41 -window Draw on a newly-created window. This is the default.
43 -root Draw on the root window.
45 -install
47 Install a private colormap for the window.
48 -visual visual
50 Specify which visual to use. Legal values are the name of a
51 visual class, or the id number (decimal or hex) of a specific
52 visual.
53 -delay microseconds
55 How much of a delay should be introduced between steps of the
56 animation. Default 25000, or 1/40th second.
57 The following six options are mutually exclusive. They determine which
59 polytope is displayed.
60 -5-cell Display the 5-cell. The 5-cell is the 4d analogon of a regular
62 tetrahedron in 3d. It has 5 regular tetrahedra as its cells,
63 10 equilateral triangles as faces, 10 edges, and 5 vertices.
64 -8-cell Display the 8-cell (a.k.a. hypercube or tessaract). The 8-cell
66 is the 4d analogon of a cube in 3d. It has 8 cubes as its
67 cells, 24 squares as faces, 32 edges, and 16 vertices.
68 -16-cell
70 Display the 16-cell. The 16-cell is the 4d analogon of an
71 octahedron in 3d. It has 16 regular tetrahedra as its cells,
72 32 equilateral triangles as faces, 24 edges, and 8 vertices.
73 -24-cell
75 Display the 24-cell. The 24-cell has no 3d analogon. It has
76 24 regular octahedra as its cells, 96 equilateral triangles as
77 faces, 96 edges, and 24 vertices.
78 -120-cell
80 Display the 120-cell. The 120-cell has no 3d analogon. It has
81 120 regular dodecahedra as its cells, 720 regular pentagons as
82 faces, 1200 edges, and 600 vertices.
83 -600-cell
85 Display the 600-cell. The 600-cell has no 3d analogon. It has
86 600 regular tetrahedra as its cells, 1200 equilateral triangles
87 as faces, 720 edges, and 120 vertices.
88 The following three options are mutually exclusive. They determine how
90 the polytope is displayed.
91 -wireframe
93 Display the polytope as a wireframe mesh.
94 -surface
96 Display the polytope as a solid object.
97 -transparent
99 Display the polytope as a transparent object (default).
100 The following two options are mutually exclusive. They determine how
102 to color the polytope.
103 -single-color
105 Display the polytope in red.
106 -depth-colors
108 Display the polytope with a fully saturated color wheel in
109 which the edges or faces are colored accoring to their average
110 4d "depth", i.e., the w coordinate of the polytope in its unro‐
111 tated position (default).
112 The following two options are mutually exclusive. They determine how
114 the polytope is projected from 3d to 2d (i.e., to the screen).
115 -perspective-3d
117 Project the polytope from 3d to 2d using a perspective projec‐
118 tion (default).
119 -orthographic-3d
121 Project the polytope from 3d to 2d using an orthographic pro‐
122 jection.
123 The following two options are mutually exclusive. They determine how
125 the polytope is projected from 4d to 3d.
126 -perspective-4d
128 Project the polytope from 4d to 3d using a perspective projec‐
129 tion (default).
130 -orthographic-4d
132 Project the polytope from 4d to 3d using an orthographic pro‐
133 jection.
134 The following six options determine the rotation speed of the polytope
136 around the six possible hyperplanes. The rotation speed is measured in
137 degrees per frame. The speeds should be set to relatively small val‐
138 ues, e.g., less than 4 in magnitude.
139 -speed-wx float
141 Rotation speed around the wx plane (default: 1.1).
142 -speed-wy float
144 Rotation speed around the wy plane (default: 1.3).
145 -speed-wz float
147 Rotation speed around the wz plane (default: 1.5).
148 -speed-xy float
150 Rotation speed around the xy plane (default: 1.7).
151 -speed-xz float
153 Rotation speed around the xz plane (default: 1.9).
154 -speed-yz float
156 Rotation speed around the yz plane (default: 2.1).
157
159 If you run this program in standalone mode you can rotate the polytope
160 by dragging the mouse while pressing the left mouse button. This
161 rotates the polytope in 3D, i.e., around the wx, wy, and wz planes. If
162 you press the shift key while dragging the mouse with the left button
163 pressed the polytope is rotated in 4D, i.e., around the xy, xz, and yz
164 planes. To examine the polytope at your leisure, it is best to set all
165 speeds to 0. Otherwise, the polytope will rotate while the left mouse
166 button is not pressed. -fps Display the current frame rate, CPU load,
167 and polygon count.
168
170 DISPLAY to get the default host and display number.
171 XENVIRONMENT
173 to get the name of a resource file that overrides the global
174 resources stored in the RESOURCE_MANAGER property.
175
177 X(1), xscreensaver(1)
178
180 Copyright © 2003-2005 by Carsten Steger. Permission to use, copy, mod‐
181 ify, distribute, and sell this software and its documentation for any
182 purpose is hereby granted without fee, provided that the above copy‐
183 right notice appear in all copies and that both that copyright notice
184 and this permission notice appear in supporting documentation. No rep‐
185 resentations are made about the suitability of this software for any
186 purpose. It is provided "as is" without express or implied warranty.
187
189 Carsten Steger <carsten@mirsanmir.org>, 28-sep-2005.
190X Version 11 5.15-3.fc14 (18-Oct-2011) polytopes(6x)