1polytopes(6x)                 XScreenSaver manual                polytopes(6x)
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NAME

6       polytopes - Draws one of the six regular 4d polytopes rotating in 4d.
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SYNOPSIS

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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DESCRIPTION

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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OPTIONS

40       polytopes accepts the following options:
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42       --window
43               Draw on a newly-created window.  This is the default.
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45       --root  Draw on the root window.
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47       --window-id number
48               Draw on the specified window.
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50       --install
51               Install a private colormap for the window.
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53       --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.
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58       --delay microseconds
59               How much of a delay should be introduced between steps  of  the
60               animation.  Default 25000, or 1/40th second.
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62       The following six options are mutually exclusive.  They determine which
63       polytope is displayed.
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65       -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.
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69       -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.
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73       -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.
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78       -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.
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83       -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.
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88       -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.
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93       The following three options are mutually exclusive.  They determine how
94       the polytope is displayed.
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96       --wireframe
97               Display the polytope as a wireframe mesh.
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99       --surface
100               Display the polytope as a solid object.
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102       --transparent
103               Display the polytope as a transparent object (default).
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105       The  following  two options are mutually exclusive.  They determine how
106       to color the polytope.
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108       --single-color
109               Display the polytope in red.
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111       --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).
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117       The  following  two options are mutually exclusive.  They determine how
118       the polytope is projected from 3d to 2d (i.e., to the screen).
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120       --perspective-3d
121               Project the polytope from 3d to 2d using a perspective  projec‐
122               tion (default).
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124       --orthographic-3d
125               Project  the  polytope from 3d to 2d using an orthographic pro‐
126               jection.
127
128       The following two options are mutually exclusive.  They  determine  how
129       the polytope is projected from 4d to 3d.
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131       --perspective-4d
132               Project  the polytope from 4d to 3d using a perspective projec‐
133               tion (default).
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135       --orthographic-4d
136               Project the polytope from 4d to 3d using an  orthographic  pro‐
137               jection.
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139       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.
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144       --speed-wx float
145               Rotation speed around the wx plane (default: 1.1).
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147       --speed-wy float
148               Rotation speed around the wy plane (default: 1.3).
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150       --speed-wz float
151               Rotation speed around the wz plane (default: 1.5).
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153       --speed-xy float
154               Rotation speed around the xy plane (default: 1.7).
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156       --speed-xz float
157               Rotation speed around the xz plane (default: 1.9).
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159       --speed-yz float
160               Rotation speed around the yz plane (default: 2.1).
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INTERACTION

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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ENVIRONMENT

174       DISPLAY to get the default host and display number.
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176       XENVIRONMENT
177               to get the name of a resource file that  overrides  the  global
178               resources stored in the RESOURCE_MANAGER property.
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180       XSCREENSAVER_WINDOW
181               The window ID to use with --root.
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SEE ALSO

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

AUTHOR

196       Carsten Steger <carsten@mirsanmir.org>, 28-sep-2005.
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200X Version 11               6.08-1.fc39 (17-Oct-2023)             polytopes(6x)
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