Hi Roger ... It sounds right. The conjecture is looking for a minimal surface area for a given volume and so the aim is for V^2/S^3 to be as high as possible. ...
Hi Roger ... I was just closing the MathWorld page when I noticed that it described Kelvin's curved truncated octahedron as less optimal than the plane faced...
Hi Adrian, ... I was thinking backwards. As it mentions later on the page the WP foam beats that number and it is a higher number. The number they give...
Hi Roger ... off_report just gives the bare ratio whereas the MathWorld figure is for the isoperimetric quotient, which is 36*PI times greater 0.0066612233 *...
Hi Adrian, ... Fumbling about in a spreadsheet I determined the reason for using 36*pi is because for a sphere (V^2/S^3)*36*PI = 1 There rounder the polyhedron...
I just found in my notes that a = 3 * 2^(2/3) is the cube root of 108. But simply cubing "a" doesn't seem to be enough. I think the components of each formula...
... I seem to be repeating something I tried last year! I found this discussion between myself and Guy, June of 2007. It may be that there cannot be integer...
Hi Carmen ... You could calculate the lengths and angles with the Antiprism programs. http://www.antiprism.com/ Here is an example showing how you would do it....
Hi Roger ... An example of a rational volume from irrational coordinates is a unit cube where you slide the vertices of the top square by sqrt(2) to the right....
Hi Adrian, ... I just noticed today that the off_trans -T command of this new off_trans doesn't change the output. I found out why. The new centre variable is...
Hi Roger ... It defaults to false here. The problem must have been a bit puzzling! I will add in your change. Adrian. -- Adrian Rossiter adrian@... ...
Hi Adrian, I decided to test the inside/outside code as the stub of a new program. I was worried about what would happen if the beginning of each face list...
Hi Roger ... Good! ... It will be interesting to see. I haven't given it much thought but I imagine that constructing the algorithm to identify the parts from...
Hi Adrian, ... the ... I have to admit I just don't get normals. ... I had thought that if one identified interior and exterior vertices, it would follow that...
Hi Roger ... The test looks like you could find the line of intersection of two face planes and then see if it intersects the edges (line segments) of either...
Hi Adrian, ... Looking at the example, I don't see anywhere that these two are not the same segments. You also mentioned about edge intersection. There could...
Hi Roger ... Whoops, I thought you were describing the tetrahedron vertices poking through the cube so I didn't run your commands! Here is an image using your...
Hi Adrian, ... Talk about rising complexity! ... I had thought bow-ties could be pre-processed into individual convex polygons. This has serious problems...
Hi All, http://www.interocitors.com/tmp/bravais.rc1.zip I put up a new bravais program. There have been extensive changes. I have placed a line at the top of...
Roger, looking forward to testing out your new bravais with some bells and whistles. when I run it, I tried -h and got the help list without any -L option for...
Hi Steve, ... I double checked the zip file and it has the RC1 version. However, there the -L options wasn't working as documented so I fixed it. (see below)...
Roger, Okay...the new bravais worked when i out it in the......bin I got the help with -L and got the other coding to work as well, and the "radial sweep...
Hi Steve, ... exploration. Well, I didn't explain why the -G 8 option completely. As the help says: -G <type> automatic grid center type (type 8 invalid for...
Roger. Loving what i see so far...the squared distance..in order and the occurences...great stuff. ... YES YES...the yin yang of these two unit cells....nicely...
Roger, cell sub-division algorithm.... 1 take any unit cell and place a cloned copy at each of its vertex. 2 remove whatever is outside the original unit cell....
Hi Adrian, ... circuits. ... I'm not quite following this. Indeed, doing this with trees is the way to do this. It is a bit like following maze paths. I think...
Hi Steve, ... For simple lattices (ex. cubic P, monoclinic P etc) the -G options already can do this. -G p (for corner) would have the vertex at the centroid...
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