--- /dev/null
+.TH XScreenSaver 1 "" "X Version 11"
+.SH NAME
+polytopes - Draws one of the six regular 4d polytopes rotating in 4d.
+.SH SYNOPSIS
+.B polytopes
+[\-display \fIhost:display.screen\fP]
+[\-install]
+[\-visual \fIvisual\fP]
+[\-window]
+[\-root]
+[\-delay \fIusecs\fP]
+[\-fps]
+[\-5-cell]
+[\-8-cell]
+[\-16-cell]
+[\-24-cell]
+[\-120-cell]
+[\-600-cell]
+[\-wireframe]
+[\-surface]
+[\-transparent]
+[\-single-color]
+[\-depth-colors]
+[\-perspective-3d]
+[\-orthographic-3d]
+[\-perspective-4d]
+[\-orthographic-4d]
+[\-speed-wx \fIfloat\fP]
+[\-speed-wy \fIfloat\fP]
+[\-speed-wz \fIfloat\fP]
+[\-speed-xy \fIfloat\fP]
+[\-speed-xz \fIfloat\fP]
+[\-speed-yz \fIfloat\fP]
+.SH DESCRIPTION
+The \fIpolytopes\fP 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 program projects the 4d polytope to 3d using either a
+perspective or an orthographic 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. Furthermore, the colors with
+which the polytope is drawn can be set to either single 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 visual 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 accoring 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.
+.SH OPTIONS
+.I polytopes
+accepts the following options:
+.TP 8
+.B \-window
+Draw on a newly-created window. This is the default.
+.TP 8
+.B \-root
+Draw on the root window.
+.TP 8
+.B \-install
+Install a private colormap for the window.
+.TP 8
+.B \-visual \fIvisual\fP
+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.
+.TP 8
+.B \-delay \fImicroseconds\fP
+How much of a delay should be introduced between steps of the
+animation. Default 25000, or 1/40th second.
+.PP
+The following six options are mutually exclusive. They determine
+which polytope is displayed.
+.TP 8
+.B \-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.
+.TP 8
+.B \-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.
+.TP 8
+.B \-16-cell
+Display the 16-cell. The 16-cell is the 4d analogon of an octahedron
+in 3d. It has 16 regular tetrahedra as its cells, 32 equilateral
+triangles as faces, 24 edges, and 8 vertices.
+.TP 8
+.B \-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.
+.TP 8
+.B \-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.
+.TP 8
+.B \-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.
+.PP
+The following three options are mutually exclusive. They determine
+how the polytope is displayed.
+.TP 8
+.B \-wireframe
+Display the polytope as a wireframe mesh.
+.TP 8
+.B \-surface
+Display the polytope as a solid object.
+.TP 8
+.B \-transparent
+Display the polytope as a transparent object (default).
+.PP
+The following two options are mutually exclusive. They determine how
+to color the polytope.
+.TP 8
+.B \-single-color
+Display the polytope in red.
+.TP 8
+.B \-depth-colors
+Display the polytope with a fully saturated color wheel in which the
+edges or faces are colored accoring to their average 4d "depth", i.e.,
+the w coordinate of the polytope in its unrotated position (default).
+.PP
+The following two options are mutually exclusive. They determine how
+the polytope is projected from 3d to 2d (i.e., to the screen).
+.TP 8
+.B \-perspective-3d
+Project the polytope from 3d to 2d using a perspective projection
+(default).
+.TP 8
+.B \-orthographic-3d
+Project the polytope from 3d to 2d using an orthographic projection.
+.PP
+The following two options are mutually exclusive. They determine how
+the polytope is projected from 4d to 3d.
+.TP 8
+.B \-perspective-4d
+Project the polytope from 4d to 3d using a perspective projection
+(default).
+.TP 8
+.B \-orthographic-4d
+Project the polytope from 4d to 3d using an orthographic projection.
+.PP
+The following six options determine the rotation speed of the polytope
+around the six possible hyperplanes. The rotation speed is measured
+in degrees per frame. The speeds should be set to relatively small
+values, e.g., less than 4 in magnitude.
+.TP 8
+.B \-speed-wx \fIfloat\fP
+Rotation speed around the wx plane (default: 1.1).
+.TP 8
+.B \-speed-wy \fIfloat\fP
+Rotation speed around the wy plane (default: 1.3).
+.TP 8
+.B \-speed-wz \fIfloat\fP
+Rotation speed around the wz plane (default: 1.5).
+.TP 8
+.B \-speed-xy \fIfloat\fP
+Rotation speed around the xy plane (default: 1.7).
+.TP 8
+.B \-speed-xz \fIfloat\fP
+Rotation speed around the xz plane (default: 1.9).
+.TP 8
+.B \-speed-yz \fIfloat\fP
+Rotation speed around the yz plane (default: 2.1).
+.SH 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 polytope 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. Otherwise, the polytope will rotate while the
+left mouse button is not pressed.
+.B \-fps
+Display the current frame rate, CPU load, and polygon count.
+.SH ENVIRONMENT
+.PP
+.TP 8
+.B DISPLAY
+to get the default host and display number.
+.TP 8
+.B XENVIRONMENT
+to get the name of a resource file that overrides the global resources
+stored in the RESOURCE_MANAGER property.
+.SH SEE ALSO
+.BR X (1),
+.BR xscreensaver (1)
+.SH COPYRIGHT
+Copyright \(co 2003-2005 by Carsten Steger. Permission to use, copy,
+modify, distribute, and sell this software and its documentation for
+any purpose is hereby granted without fee, provided that the above
+copyright notice appear in all copies and that both that copyright
+notice and this permission notice appear in supporting documentation.
+No representations are made about the suitability of this software for
+any purpose. It is provided "as is" without express or implied
+warranty.
+.SH AUTHOR
+Carsten Steger <carsten@mirsanmir.org>, 28-sep-2005.
projects / xscreensaver / blobdiff