You probably haven’t noticed the absence of a link in the upper left, “buy 2D printed objects”, which went to my catalogue on Zazzle: shirts, mugs, posters. The number of sales I made through that was not zero, but it was far smaller than the number of things I bought myself!

Four years ago MC Escher’s heirs complained that my descriptions of two shirt designs included language like “The underlying geometry is closely related to that of Escher’s Circle Limit series,” so Zazzle hid them until I removed Escher’s name. No, wait, they didn’t do that, they irrevocably deleted the designs without warning, saying (until I raised a fuss) only that they violated an unspecified copyright.

Last week my step-family had a gathering at a resort in the Rockies, and I ordered a personalized mug for each of them. (Here is a hint at what they look like.) Zazzle was unhappy with the address I gave, but both Google and Apple Maps recognized it, so I said go ahead. When the package reached the town, it was bounced back for “insufficient address”. I then learned from the lodge’s owner (indirectly, through the family member who booked it) that USPS does not deliver to that street. (I wish I’d thought of General Delivery.) Fortunately this was well before we were due to get there. I suggested to Zazzle that, when the package came back, they try FedEx or UPS. They instead reprinted the order and sent it by Express Mail.

I go to the gathering, stay for a largely miserable week (insomnia), come home. Two days later, some iteration of the order is successfully delivered, I don’t know how. (The order’s tracking link shows only the first attempt.) So now the mugs are cluttering up a stranger’s kitchen; I hope the stranger finds them pretty. I point out to Zazzle that I told them twice that I wanted the package to arrive no later than Friday July 19. They tell me how to return it. I explain that everyone I know left that county on Saturday morning; I will not ask the lodge’s owner or the new occupants to do my errands.

We are really sorry about the various issues you have had, we would really appreciate the chance to try and make this right.

Please let us know if there is anything at all we can do for you. If you have any further questions or concerns please respond directly to this email and I would be happy to assist. Thank you for visiting Zazzle.

I don’t see how it can be made right. They can send mugs to the intended recipients separately, but I’d rather wait for the next gathering and present them all at once.

So. I haven’t tried Cafepress, and there must be other similar services. Have you experience with any of them?

I got a notice from Zazzle that if I don’t post at least one new product in every fifteen months they’re going to charge me a Non-Contributing Account Fee. So here’s one. I can spin more variations on this theme until the cows come home.

Sometimes I search my blog for this picture and scratch my head in puzzlement that it’s not here, before remembering that I posted it on Google Plus back when I used that.

So here it is. Stephen Guerin (the shaven one) displays his canvas print of one of my designs.

The colors came out better than I hoped, in stark contrast to a couple of mugs with related designs that I got from the same shop.

I’ve had other designs made in steel but not this one. (The sintering leaves the steel highly porous, so liquid bronze is brought in by capillary action to fill it; the result is about three parts steel to two parts bronze – if I understand right. Hence the color.) (Later: I was mistaken: the steel powder is not sintered but glued; I guess the bronze burns away the glue.)

While it was on its way to me, I thought of some improvements. ( . . more . . )

I’ve been designing printable models of the Lawson-Klein surface

To minimize the distortion of the projection, I want the projection center to be as far as possible from the surface. One thing I tried was pursuit: starting with an arbitrary point P in S3 and an arbitrary point L(u,v) in the surface, move (u,v) to bring L closer to P while simultaneously moving P away from L. This gets me nowhere so far: either it fails to converge or P converges to the antipodes of L, which is also in the surface (change u by π).

My newest design on Shapeways is a model of the Lawson-Klein surface : a stereographic projection of

( cos(u)cos(2v), cos(u)sin(2v), sin(u)cos(v), sin(u)sin(v) )

I noticed that Shapeways had 13 models of the roundest of the fullerenes (one of the 1812 forms of C60), but none of the less regular forms; so I made some.

Each of the white pieces has mirror symmetry; the red pieces are chiral. Not shown (because it hasn’t been printed yet): the blue set, which is a reflection of the red set. The idea is that you buy both red and blue if and only if you count reflected chiral forms separately.

These figures have 12 pentagons and up to 8 hexagons. They include the two smallest forms with no nontrivial symmetries, and the two smallest with no ‘peaks’ where three pentagons meet.