Hi Steve ... Not without using a sphere radius that causes overlap of the outer spheres. ... No, that would involve increasing the length of the minimum edge,...
Hi Rybo ... People can't get to your file by clicking on the link in Yahoo's message at the Yahoo site because the URL is too long (for Yahoo). If you put your...
[That last line in my last message was intended to be, "Must be a reaction to the rapid increase in hard drive storage *prices*.... just kidding." ] Anyway,...
I ran a couple of small checks on the cell volumes and resulting Voronoi densities I've been getting from SpringDance + Python + Qhull and it looks good. But...
Adiran, Thanks for your assessment of my "re-positioning" question. re your message 11411....[ the posted inot distances ] I stll am having a problem though. ...
John, Do you have edge/seperation data for your teticosaX, etc ? What about making up their duals ? [ and yes, the edge data would be very nice too ] Question:...
When a person can register a domain name for eight bucks a year (goDaddy, for ex.) and get 50 megabytes of webspace along with FTP, email addresses and other...
From: "John Braley" <tau@...> Subject: Re: [synergeo] Re: Densities ... I'm pleased to see that this offset, which is in the OLJ i(not), shows up also in...
I offer numbers from something we've not yet done (TMK). These objects have "gaps." (Wire-framed, we might call them 'non-unit edge excess', or overage. If...
Hi Steve ... In the dual I made I "pushed" the spheres out so they lay on the same sphere as the original outer spheres (radius 10 through the centres). Here...
Adrian, Yes, this looks really good now. Nice inclusion of the face data too. My limited experience with waterman duals did not find any edges of integer root...
Hi Steve and All ... I should confess that I still don't know how to make a "true" dual for an irregular poly (no answers when I asked here before). Obviously...
... Here is an example, what is the dual of a regular tetrahedron with one vertex shaved off (i.e. a tapered triangular prism)? I guess it would be something...
JB and Adrian, Here is a dual reference - http://home.connexus.net.au/~robandfi/PolyNav/PolyNavigator.html Jim Lehman also posted a clear definition and book...
Hi Steve ... Thanks for the link, just what I was looking for. The method doesn't look too difficult to implement. I'll try it and see how it goes for the ...
Adraian and JB, Here is Jim's reference... Duals are formed by joining a point that is perpendicular above the center of each face to equivalent points above...
Hello, This email message is a notification to let you know that a file has been uploaded to the Files area of the synergeo group. File : /Rybos...
synergeo@yahoogroups....
Aug 1, 2003 10:14 pm
11441
That's the method -- and a good reference. In Great Stella it's called "spherical reciprocation"; I think it also goes under a name such as: "polar duality",...
Yes, big difference. This method doesn't work for many polyhedra. For starters, when you get to the "center of each face" part, you ask, unless the face is ...
John, Adrian, JB, Here is a quote from an email Rob Webb ( Great Stella creator) sent to me some while ago... "There is no definite way of choosing a centre or...
Steve, In this case, I think even Rob would agree with you and pick the center of the center ball (because the other 12 points are on the surface of a sphere...
Synergeticists, Im going out on a limb here --not that i havent already for some time-- and say that the 6 great circles of the ico are the basis of the ...
John, you wrote- Rob begins his section on duals with a questionable statement: "For any polyhedron, there exists another polyhedron which is its dual." Can...
... In 4-D, duals are formed by joining a point that is in the center of each polyhedron to equivalent points in the centers of all neighboring polyhedra. The...
... The description at Bourke's site is only for regular polytopes. "Joining a point that is in the center of each polyhedron to equivalent points in the...
... Yes, that's true. As far as duals are concerned, only the TOPOLOGY matters. How can you define a "center" if the polytope (polygon, polyhedron, etc.) is...
Alan wrote, in part: "Yes, that's true. As far as duals are concerned, only the TOPOLOGY matters. How can you define a "center" if the polytope (polygon,...
