lafite "orbifold-notation"

at a shell prompt, but replacing orbifold-notation with a valid
notation, in Conway's system.  You should put double quotes around it,
since some of the symbols used in the notation have special meanings to
the shell.  

A complete notation is somthing of the form:


a  is typed as `o' and represents a handle in the orbifold.

a  is a digit 2 through 9, or `i', representing a cone point of
order 2, 3, etc, or infinity.  

a  is a star, typed `*', possibly followed by some
digits (with the same understanding about `i').

a  is typed as `x', and represents a corss-cap on the orbifold.

Some nice notations to play with are:  237, *237, 345, *345, o2, oo,
23*, 3*x, iii, etc,.  Things with a very negative Euler number tend
not to be too interesting, since everything disappears into the
distance very quickly.  

In theory, _any_ orbifold notation should work, but right now, things
with lots of `i's don't work (this a fairly minor bug).  


First things first:  to quit, hit the escape key.  If the system gets
massively loaded, and you've no idea what's going on, this is always a
good option.

If all goes well, you should see some informatio about the orbifold
you typed in, like it's Euler number, and how many length and twist
parameters the Teichmuller space has.  Then two windows should pop up.
One is the drawing window, while the other contains a toolbox.  

The drawing window should start up blank, exect for some black and red
lines (``the grid'').  

The tools work pretty much as in a simple drawing program with the
following ``intuitive'' conventions:

To draw a line or polygon, select the line or polygon tool, and use
the left mouse button to place points.  To complete the figure, click
the middle mouse button.

To edit a line or polygon, select the pointer tool, and use the left
mouse to select the thing you want to edit.  Use the middle mouse
button to move control points.

IMPORTANT FACT:  You can only edit the ``original'' copy of something
you've made.  If you don't remember which is the original copy, hit the
down arrow key until only one copy is left.  See below.  This is one
reason why the grid is useful, since if you draw stuff in the red
part, you'll never get confused about this.

To zoom in/out, use the magnifying glass tool.  The left mouse button
goes in, the right goes out.

To rotate an object, select it with the pointer, then use the rotate
tool.  Click with the left button to position the center of rotation,
then click and drag to rotate.  This tool is a little flaky.

The reflect, circle, and rectangle tools don't work.  (Sorry:  no time)

The hand tool moves what you are looking at.

To edit a color, click on to depress the color button, then click
again.  A color editing window should pop up.  A truly cheesy hack:
the background color is the ninth color up from the bottom.  For
printing out in b&w, it's best to set this to white.  (The default is
light gray.) 


Holding down the right mouse button in the drawing window, you should
see a menu that looks like:

		model 		>
		twist		>
		length		>
		toggle grid
		draw more	
		draw less
		set prune radius
		bring to front
		send to back

The three models avialable are Poincare (inversive), Projective, and
Upper Half Plane.  The UHP model is a bit flaky.

To draw more group elements, select ``draw more'', or hit the up arrow
key.  ``draw less'' = down arrow.  

You use the twist and length menus to fiddle with the parameters in
the orbifold.  The menus should show how many paramters the orbifold has,
say, 2 twists, and 2 lengths.  You select which one you want to change,
using the menu, and then adjust it with the left and right arrow keys.
Admittedly, this is not the optimal way to do this.  The arrow keys
currently change the paraters by 0.1.  You want to change the delta?
no problem, just re-compile!  

It's best to turn down the number of group elements before fiddling
with the parameters, otherwise you can sit around for a while,
wondering what's going on.

The grid can be useful for getting things correctly aligned at cone
points, etc,.  The dotted lines correspond (more or less) with length
parameters, and show how the orbifold was decomposed.

print outputs a color PS file called ``'' into the current
directory.  open... is unusual in that it doen't clear what you have
already  (the escape key does that :-) )

And that's more or less it.  Any questions or bugs?  email me at:

or, in 1993-4, at: