(He knows about Scherk surfaces.) ---------- Forwarded message --------- From: john graham <ikojag@yahoo.com> Date: Wed, Apr 24, 2019 at 10:12 AM Subject: Re: Infinite Mobius To: Bill Gosper <billgosper@gmail.com> Hello Bill. The Gyroid is indeed a wondrous fascinating shape, it is evidently non self-intersecting and has the potential for infinite growth through the repeated addition of identical forms. However I see that it is a surface of two opposite faces that divide space into two opposite but mutually exclusive and interlocking labyrinths. In its developed state it is edgeless. My object, on the other hand, is monospatial and is clearly a single surface as can be demonstrated locally and elementally, such as to infer that the single surface could be repeated ad infinitum. The object consists of twisted octagons interconnected four ways along a three dimensional cubic lattice grid, with the result that the edges are related helical lines of a fixed and regular period. I'd be interested to find out if the object is related to any of the known mathematical surfaces. John.. On Tuesday, 23 April 2019 18:12:24 BST, Bill Gosper < billgosper@gmail.com> wrote: Can you explain your object compared to https://en.wikipedia.org/wiki/Gyroid ? —Bill On Tue, Apr 23, 2019 at 5:23 AM john graham <ikojag@yahoo.com> wrote: Hello Bill, I browsed through Shapeways catalogue, and homed in especially on complex surfaces. It was really very interesting. In fact I've ordered a Scherks First surface, a fascinating shape in itself and one that comes pretty close to what I've created/discovered? but clearly is not. I am sending you some images of the two models that I have made by hand one of which I've resolved into equilateral triangles. Inevitably any embodiment or manifestation of the infinite Mobius will be a fragment, as is shown here, but under certain geometrical conditions the loose ends can be tied up to unite the edges into a single entitiy, so that the mathematical integrity of the Mobius (singe edge/single surface) is maintained. I apologise if the images take some working out. My workmanship is less than perfect, and I do not, at present. have the IT skills to produce CGIs, but nevertheless I look forward to hearing from you. John.