Photo credits: Nancy Rose Marshall. All photos were taken on May 10, 1999.
Above and below are pictures of a large version of the
Hull-Ow
Five Intersecting Tetrahedra. They were
folded from large sheets of Strathmore paper. (I think.)
This is a spherical Buckyball made from 360
Pentagon-Hexagon Zig-Zag Units
(PHiZZ Units). The coloring is derived from a proper 3-coloring of the edges of
this polyhedron. I made a proper 3-coloring of the edges and then
used two of the colors to decompose the vertices of this polyhedron
into disjoint even cycles. I then colored these cycles monochromatically
to see what they looked like. I tried to alternate the cycles in lime green
and purple-blue so that one could see how they intertwine and nest
within each other. But they turned out to be so complicated that I would
have needed several colors to highlight them all properly.
Here is another Buckyball, this time from 810 units. This one is
properly 3-edge colored, and I've included a Photoshop-altered
version of this picture in an attempt to highlight the disjoint
even cycle decomposition induced by the green and blue edges.
This is the largest Buckyball I've made from the PHiZZ unit.
This was a work-in progress back in May of 1999, attempting to make
a modular origami torus using PHiZZ units. I did this by using pentagons
spaced out along the "outer rim", and opposite these pentagons I put
heptagons along the "inner rim". The heptagons provided the negative
curvature needed to make the inside part of a torus. I've since
completed the project, but don't have any pictures of the finished
torus. (Yet!) The final torus had 10 pentagons, 10 heptagons, 60 hexagons,
and required a total of 660 PHiZZ units. I imagine that smaller tori
are possible (although you can prove that you'll always need an equal
number of pentagons as heptagons), but I haven't tried making one
yet. Other people have, though!
Roberto Gretter of Italy has made a very nice torus from only
555 PHiZZ units.
Take a look at it on his web page.
Hey Sonobe unit fans! If you haven't tried making this from
Sonobe units, you really should try! It's a dodecahedral spikey
thing (I can't think of any good technical name -- it's neither
a stellation nor an augmentation of one of the classic polyhedra)
made from 60 Sonobe units. Yes, if you look carefully you can see
that the Sonobe units need some alternate creases to form
this shape, and I highly encourage everyone to figure it out!
I can't remember where I first saw this Sonobe unit construction,
but it was probably from Michael Naughton back in the late 80s.
