4/23/93.  A copy of the still-in-progress SnapPea 2.0 is included.
It computes symmetries and isometries of all cusped hyperbolic
3-manifolds, even those whose canonical cell decomposition
is not a triangulation.  It also lets you permanently fill in
cusps, and drill out geodesics to create new cusps.

Added 5/18/92.  In this version of snappea the "pretty pictures" program
has options which number the horoballs and the edges of the boundary
triangulation, and automatically write the diameters of the horoballs
and the lengths of the edges to files called "horoballs.out" and "edges.out".

Hints for using snappea.

(0)  You should begin by copying the Snap Pea folder onto your hard disk.
(Snappea will want to access the documentation files and the files
containing dehydrated libraries of manifolds.)  If you got Snap Pea via
ftp for use on a Macintosh you will find that the unstuffing process
randomizes the position of icons in windows, so please don't attach
any significance to their appearance.

(0.5)	Snappea now creates color graphics.  It uses 32-bit QuickDraw
which comes built-in to System 7.0, and is also included in the ROM
on the newer Macintoshes.  If you have an older Macintosh and are
using System 6.0.x, you may need to drop 32-bit QuickDraw (provided
with snappea) into your system folder.  If you're not sure whether you
have it or not, just go ahead and start using snappea.  If you don't
have 32-bit QuickDraw, when you go to draw a Dirichlet domain or
horoball packing, snappea will print an error message and quit.

(1)  The standard version of snappea requires an SE/30 or almost any
model Mac II.  (The reason is that snappea has been compiled to make direct
calls to the 68881/68882 floating point coprocessor.  This speeds up the
computation of hyperbolic structures enormously.)
	If you have a Mac512K, MacPlus, MacSE, MacClassic or MacIIsi without
a coprocessor, you should have received the version called "snappea
MacPlus" which does not require the coprocessor.  Snappea is pretty
sluggish on a MacPlus, though, so if at all possible I recommend you try
to arrange the use of a Mac II or SE/30.

(2)  The programs "snappea" and "snap pea" are different!

	Snappea is a command line driven program which offers all
currently available features.  To learn to use snappea you can work
through the "snappea tutorial" found in the documentation folder.

	Snap pea employs a standard Macintosh interface.  To use it, simply
start it running and explore the various menu commands.  Note that in
snap pea, unlike snappea, you may simultaneously open many different
windows of many different types.  There is
no need to read any documentation ahead of time.  The few points which
are not obvious are explained by "Help..." menu commands.  At present
snap pea does not yet include all of snappea's features (e.g. it cannot
test for isometry, cannot compute fundamental groups, cannot draw
horoball packings or Ford domains, etc.) so for these features you should
still use snappea.

(3)  The nongraphical parts of snappea are portable.  Snappea knows
whether it's being compiled on a Mac or not, so the same source
code can be used without modification on UNIX systems as well
as Macs.  A completely rewritten SnapPea is now under construction.
The new SnapPea will have a platform-independent computational
kernel, complemented by several user interfaces (Mac, X-Windows &
NeXT will be the first GUIs).  Suggestions for the new SnapPea
are eagerly solicited.

(4)  The source code folder contains .c files, .h files, a THINK C 5.0
project document, and a UNIX makefile.

(5)  The "tables" folder contains some tables listing invariants for
the "census" manifolds.  These tables are useful if you want to check
for a manifold with given invariants.  The following files are included:

"five.summary", "six.summary", and "seven.summary" list basic invariants
	for all cusped hyperbolic 3-manifolds obtainable from 5 or fewer
	tetrahedra, and all orientable cusped hyperbolic 3-manifolds
	obtainable from 7 or fewer tetrahedra.

"CS tables (census)", prepared by Craig Hodgson, is similar to
    five.summary except that it also includes 12 times the Chern-Simons
    invariant, and nonorientable manifolds are excluded.

"CS tables (closed) [short]" (also by Craig Hodgson) list invariants for small
    volume closed orientable 3-manifolds obtained by Dehn filling the census
    manifolds. This list is an essential guide for exploring low volume closed
    hyperbolic 3-manifolds because it gives you the Dehn filling coefficients
    for obtaining the closed manifolds from the cusped census manifolds.
    The list is actually an initial segment of a much larger (525K) file.

"link symmetries" lists the hyperbolic volume, symmetry group, chirality,
	and invertibility of knots to 11 crossings; and the hyperbolic
	volume, symmetry group of link, symmetry group of complement, and
	chirality of links to 10 crossings.  (SnapPea also tells you how
	each symmetry acts on the link components, but this information is
	omitted from the table to save space.)

"11cKnot-10cLink_index" is Joe Christy's index to the 11 crossing
	knots and 10 crossing links.

Note:  You can read these tables with TeachText, but the spacing doesn't
come out quite right.  If possible you should use some other word processor
which supports a monospace font like Monaco.

(6)  The Multifinder partition size is initially set to 1400K to allow for
large manifolds.  You can make it smaller or larger as necessary.  In
particular, the 384K default partition size works fine.

(7)  You can't read the files snappea produces (e.g. the manifold files,
the files of generators, etc.) by double-clicking them on the Mac.  The
reason is that they are not associated with any particular word
processor.  To read them, first start your favorite word processor
(any word processor will do, including TeachText), and then open
snappea's files from within the word processor (choose Open... from
the File menu).
	For documentation on file formats, please contact me.

(8)  Please let me know about any bugs you find.  More generally, I'd
like to hear any and all suggestions you have (major or minor) for
improving this program and/or the documentation.  Please send comments
and suggestions (and questions, if you have any) to weeks@geom.umn.edu
or Jeff Weeks, The Geometry Center, 1300 South Second Street,
Minneapolis, MN 55454.

Have fun.

Jeff Weeks 2/29/92