(You can find other related messages by going to the ORIGAMI-L archives
 at http://origami.kvi.nl and searching for "flower tower" in early
 1998.)

Date: Sat, 21 Feb 1998 01:27:11 -0500
From: Thomas C Hull 
Subject: Re: Help! Flower Tower

Salve!

John Marcolina asked how to fold more than 2 levels in Chris
Palmer's 8-petal (octagonal) flower tower.  Realizing full
well the dangers in trying to explain a complex infinite
progression fold like this in ASCII, I'll give it a try.

The key that you're missing is understanding how the creases
work from one level to the next.  The same process is at
work in the 8-petal version as in the 5-petal one.  (Although
the 5-petal one looks a bit simpler.)  So one thing you
might want to try to do isreally study how the multiple
levels fit together in the 5-petal version, and then try to
do a similar thing for the 8-petal one.  That's not
much help, I know, so ...

>>>
I tried following the same procedure as in Chris video - forming all the
creases, then collapsing starting in the middle and working my way out.
<<<

Well, this is one approach you can take, but it is very
difficult.  It can look like it has to be 3D between levels,
but that's only because you're going from the inside-out.

When I teach the 8-petal version to people, I like to
go from *the outside-in*.  This can be done by "decreeping",
a term that Chris and Jeremy Shafer have popularised.  I'll
try to describe it, but be warned that this won't be easy to
follow:

Start by folding an octagon twist (the standard, closed-back one).
Got that?  Good.  Now, twist the octagon in the *opposite*
direction by 45 degrees.  That is, if the octagon twist
is clockwise, ratate the octagon by 45 degrees in the counter-
clockwise direction.  This will create little zig-zag pleats
under the octagon.

Now, doing one at a time, bring each corner of the octagon to
the center of the octagon.  The pleat under the octagon's corner
should do 1/2 of a petal fold.  Crease firmly and unfold.
Then repeat this with all the other corners of the octagon.
(In fact, you can do them all at once, making a strange
purse variation.

Anyway, that last step will crease a smaller octagon inside
the octagon twist, and this smaller octagon is all valley
folds, right?  You want to *decreep* this inner octagon.
That is, open up the model, turn the inner octagon valley creases
into mountain folds, and recollapse.  This will force the inner
octagon to make a new, smaller octagon twist on top
of the first one, and will result in a level one 8-petal
flower tower.

Of course, it's not as easy as all that.  The decreeping process
involves rearranging a lot of other creases to collapse it.
In particular, remember the 1/2 petal folds we made while
"pursing" the first octagon twist?  The half that's folded
"in" of these petal folds needs to be unsunk - and this actually
creates the 8 petals of the first level.

Once you've mastered all that, the next level is easy.  Purse
the smaller octagon in the same way and decreep it.  Yes,
this means you gotta open up the first level to get your
nimble fingers inside to arrange the second level.  But
once you see how the collapsing process works, it get easier
to recollapse everything.  Then do the 3rd, 4th, 5th, ...
levels in all the same way!

Once you have all that down, try dodecagon flower towers!

--- Tom "that's my leg you're pulling!" Hull
    Somerville, MA
    thull@merrimack.edu
    http://www.math.uri.edu/~hull