-
Daniel Wyllie Lacerda Rodrigues's video of truncated octahedra (2.2 MBytes),
April 2007.
Before obtaining a copy of my book,
Daniel Wyllie Lacerda Rodrigues (in Brazil) rediscovered the 9-piece hinged dissection
of two truncated octahedra to one that I mentioned
at the top of page 201.
He produced an earlier video with the same basic idea
back in June 2006, with his enthusiastic hamster running
around on a wheel in the background.
Now the hamster is gone, but the model is nicer,
with pieces in two colors,
which really set off the symmetry!
-
Daniel Wyllie Lacerda Rodrigues's video of truncated octahedron to hexagonal prism to triangular prism,
November 2011.
In November 2011, Daniel Wyllie Lacerda Rodrigues (in Brazil)
alerted me to a video that he had shot of a 3-way hinged dissection
of a truncated ooctahedron to a hexagonal prism to a triangular prism.
The 18-piece dissection is very symmetrical and is derived from
Anton Hanegraaf's hinged dissection of a truncated ooctahedron to a hexagonal prism
as illustrated in Figure 20.4.
What a lovely extension!
-
Walt van Ballegooijen's videos of his hinged linkage for a 2x1x1 rectangular solid to a cube:
first movie (4.6 MBytes)
and second movie (4.6 MBytes),
February 2008.
Walt van Ballegooijen (in the Netherlands) modified Anton Hanegraaf's hinged dissection of a 2x1x1 rectangular solid to a cube
to produce a remarkably symmetric hinged dissection,
as I discuss on
a page in my photo gallery.
-
Robert Webb has a nifty video of his hinged linkage for a regular dodecahedron to a rhombic dodecahedron on his
Dodecahedron Shape-shifter webpage.
Actually, there is a hole in the rhombic dodecahedron in the shape of the tetrahedral stellation of the regular dodecahedron,
as Robert points out.
(Thanks to Joe Malkevitch for bringing Robert's webpage to my attention!)
-
Dirk Huylebrouck has sent me links to two videos shot by his students at Sint Lucas (Brussels, Belgium)
that he uploaded to YouTube.
The videos are of models of twist-hinged benches that I had presented at
the Bridges Donostia conference in Spain in July 2007.
The links plus some general explanation is on
this page.
-
The Elica Team has combined an animation of the swing-hinged dissection of an
equilateral triangle to a square with musical accompaniment
and eight Japanese haiku.
They call it "The Convertible House".
You can find a link here.
-
The D*Haus Company Ltd has designed the D*Table,
a rotatable, flexible and highly interactive piece of furniture
constructed using Corian on the surface, in a wide range of possible colors.
Take a look at it here.
The company has also designed a hinged house, as you can see in the
BBC video from "The One Show".
The cost of the actual house (not the mock-up that they play with in the video)
is a cool £800,000 to £1,000,000 as of May 2014.
That's pricey(!), but what do you expect for a house whose rooms can track the sun?
-
Izidor Hafner,
in the Department of Mathematics at the University of Ljubljana in Slovenia, posted
an intriguing video (5.2 MBytes) on his website.
The video shows the flexing of a nonconvex solid of 60 isosceles triangular faces
that when in the most symmetric configuration looks a lot like the small stellated dodecahedron {5/2,5}, which is based on 12 pentagrams.
Each isosceles triangle is hinged to three other triangles by piano hinges along its edges.
Unlike small stellated dodecahedron, which has its visible portions being isosceles triangles with edges in the ratio of approximately 1.618,
the solid in the video has isosceles faces with edges in the ratio of 2.
Izidor says that more likely that his solid is only infinitesimally flexible.
As discussed in "Turnabout 5", a theorem by Connelly, Sabitov, and Walz establishes that when a flexible polyhedron flexes,
its volume does not change. Can you see this in the video? It's difficult to see.
-
Here's another equilateral triangle to square video here.
Thanks, Alejandro! That's a nice mention for my second book!
Thanks to Daniel Wyllie, Walt, Izidor, and the students at Sint Lucas
for allowing me to post their movies.
They retain all rights to them.
Last updated October 28, 2015.