"Hi Joe,"
"You fiend! I looked at that site and have become fascinated with
these things -- way cool. I just wish I had more hours in the day
so I could play more and still get my job done."
"Thank you!"
Bruce B. - Photographer, S.F. Bay Area
Hexahexaflexagon Sighting Over Astoria!
"... with the hexahexaflexagon (six faces), you will always
occasionally get "stuck"--there will be creases on some faces
that don't open. The user will have to rotate the flexagon and
fold along the other set of creases on the face. Have you really
folded a hexahexaflexagon that never gets 'stuck'?" -- Ann
YES !!! ( see story below )
NOTE : A disassembled one is pictured here in a scan - the faces
are 1,2, and 3. IF it's unfolded WITHOUT rotation, then face 1
produces "4", face 2 produces "5" and face 3 produces "6" ! Also
any unfolding continues on and on, without end, just the three
'extra' faces take positions in the loop of "three" ...
The faces rotate this way :
1-2-3 loop
4-3-1 loop
5-1-2 loop
6-2-3 loop
I suppose I've invented the hexahexaflexagon Altieri variation,
but really it would be a tetra-hexahexaflexagon -- so perhaps
my cousins back in 1969 were close to the truth, but those did
get stuck, as do other hexahexaflexagons I've ever seen ...
Below is the scan, with numbered faces, of my last one - I think
this is the one from 1939, and somehow the end folding/gluing did
end up wrong ever since - it truly alternates 4 leaves - 2 leaves
While it hasn't been seen in over 45 years, first sighted
in the '30s, here's today's new sighting ... enjoy!
Here's my story : I first saw one of these near Bayside
Elementary School in the late 1950's or early 1960's -
I misremembered the name, but it turns out to be a
hexahexaflexagon.
My cousins and I managed to make a few, and I always kept
one over the years. Eventually I gave away my last one,
by accident, and never could recreate the pattern again :(
An Internet search a few years ago resulted in nothing,
and from time to time I would take a strip of 'adding machine
tape' and try again. Having 90/45/45 degree triangles would
always fail, so I reasoned yesterday that a hexagon has 6
sides, so 360 degrees divided by 6 yields 60 degrees, or a
60/60/60 equilateral triangle! The other missing part is that
there are 18 triangles in a strip, or the "six" times three -
three is how many different sides repeat in the continuous
unfolding of the triangle 'strip', as you can start numbering
the corners as you unfold, and after the third new faces
appear, it repeates with the first - so it's only seemingly
an infinite unfolding, but really a loop of '3'.
After much folding in a 'snake', and a rotating roll 'around
a pole', the continuous strip eventually folds again ( 4-2-4-2
etc ) to create the outer hexagon shape. If all goes well,
and the ends are attached, a loop, like a mobius loop, is made ...
Below is a 3D simulation of the unfolding, and plans to fold
your own, as the 'Net now has grown to include things so
obscure, and nearly forgotten! Enjoy!
folding instructions HERE
More instructions *HERE*
3D JAVA Simulation HERE
