On 2015-06-12 13:30, Bill Gosper wrote:
Questions: Exactly what happens to the iso"perimetric" quotient when you delete the interior faces of a Weaire-Phelan unit cell? (For all distinguishable translations.) What is the exact, analytic quotient for Kelvin's cell? (The ISCs don't even recognize 64*π/3/(1 + 2*Sqrt[3])^3.) (Shudder) ditto for the Weaire-Phelan? --rwg
Wow, no takers. I bet it's a toughie. Anyway, I was lucky enough to visit Nathan Myrhvold's superhouse, which is wall-to-wall aperiodic, waterjetted from large slabs of semiprecious minerals, except glass where you can look down at the indoor pool. Floor to ceiling, the walls are aperiodic wooden lattices and panels. Need I describe the ceilings? Indeed, even the bathroom drain grates. (As George suggested. But unsymmetrical. The tilings are all original.) And the huge metal gate and inner door, and the rolling gate at the street,... Jennifer Chayes calls it a grand mosque. Nathan calls it the house that Mathematica built. Visiting Stephen Wolfram sniffed, "Well, I live in the house that Mathematica *paid for*." --rwg
On 2015-06-10 18:37, James Propp wrote:
Where do things stand now? Is it still possible to get pseudo-aperiodic toilet paper?
And while we're on the subject: do Weaire and Phelan have any kind of copyright on the Weaire-Phelan structure that they discovered (subsequently incorporated into the Water Cube in Beijing)?
Jim Propp
On Wed, Jun 10, 2015 at 8:48 PM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
I regret to have to confess was the culprit responsible for designing the modified tiling (periodic along one axis) --- ah --- behind this particular contribution to the artistic life of the twentieth century.
Not for the first or last time, I failed received so much as a letter of thanks from the commercial enterprise concerned. [Though I was subsequently obliged to --- er --- come clean to Penrose about my part in the affair.]
Moral: if you are approached by an individual with an enquiry of a suspiciously industrial nature, get things --- um --- down on paper beforehand!
Fred Lunnon
On 6/11/15, James Propp <jamespropp@gmail.com> wrote:
Was all the Penrose tiling toilet paper manufactured by Kimberly Clark in the late 90s destroyed, or does some of it still survive?
If there are still rolls out there, and the price isn't prohibitive, you could install some (presumably for display purposes only) elsewhere in the bathroom.
If you don't know[ꞥ] the story of Sir Roger's lawsuit against Kimberly Clark, I urge you to look it up. It features one especially memorable quote, from David Bradley: "When it comes to the population of Great Britain being invited by a multinational to wipe their bottoms on what appears to be a work of a knight of the realm without his permission, then a last stand must be made."
Jim Propp
On Wednesday, June 10, 2015, Dirk Lattermann <dlatt@alqualonde.de> wrote:
Finally, a year after we moved into our new (old) house, I managed to finish the penrose mosaic for the shower in our ground floor bathroom.
I put two quick pictures, before the glass wall was installed, at
http://folgenschwer.de/mosaik/
Thought some of you might enjoy, Dirk
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