1polytopes(6x)                 XScreenSaver manual                polytopes(6x)
2
3
4

NAME

6       polytopes - Draws one of the six regular 4d polytopes rotating in 4d.
7

SYNOPSIS

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

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
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

OPTIONS

40       polytopes accepts the following options:
41
42       -window Draw on a newly-created window.  This is the default.
43
44       -root   Draw on the root window.
45
46       -install
47               Install a private colormap for the window.
48
49       -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
54       -delay microseconds
55               How much of a delay should be introduced between steps  of  the
56               animation.  Default 25000, or 1/40th second.
57
58       The following six options are mutually exclusive.  They determine which
59       polytope is displayed.
60
61       -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
65       -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
69       -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
74       -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
79       -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
84       -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
89       The following three options are mutually exclusive.  They determine how
90       the polytope is displayed.
91
92       -wireframe
93               Display the polytope as a wireframe mesh.
94
95       -surface
96               Display the polytope as a solid object.
97
98       -transparent
99               Display the polytope as a transparent object (default).
100
101       The  following  two options are mutually exclusive.  They determine how
102       to color the polytope.
103
104       -single-color
105               Display the polytope in red.
106
107       -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
113       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
116       -perspective-3d
117               Project the polytope from 3d to 2d using a perspective  projec‐
118               tion (default).
119
120       -orthographic-3d
121               Project  the  polytope from 3d to 2d using an orthographic pro‐
122               jection.
123
124       The following two options are mutually exclusive.  They  determine  how
125       the polytope is projected from 4d to 3d.
126
127       -perspective-4d
128               Project  the polytope from 4d to 3d using a perspective projec‐
129               tion (default).
130
131       -orthographic-4d
132               Project the polytope from 4d to 3d using an  orthographic  pro‐
133               jection.
134
135       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
140       -speed-wx float
141               Rotation speed around the wx plane (default: 1.1).
142
143       -speed-wy float
144               Rotation speed around the wy plane (default: 1.3).
145
146       -speed-wz float
147               Rotation speed around the wz plane (default: 1.5).
148
149       -speed-xy float
150               Rotation speed around the xy plane (default: 1.7).
151
152       -speed-xz float
153               Rotation speed around the xz plane (default: 1.9).
154
155       -speed-yz float
156               Rotation speed around the yz plane (default: 2.1).
157

INTERACTION

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

ENVIRONMENT

170       DISPLAY to get the default host and display number.
171
172       XENVIRONMENT
173               to get the name of a resource file that  overrides  the  global
174               resources stored in the RESOURCE_MANAGER property.
175

SEE ALSO

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

AUTHOR

189       Carsten Steger <carsten@mirsanmir.org>, 28-sep-2005.
190
191
192
193X Version 11               5.15-3.fc14 (18-Oct-2011)             polytopes(6x)
Impressum