Re: tri-hubs and quad-hubs ?

["J. Michael Rowland" <jmr at marathoncomputer dot com>]

domesteading-request at sculptors dot com  Sat Jul 14 17:00:42 2001 wrote:

> How about the hubs to make a rhombic dodecahedron ?
> This would require 8 tri-pod hubs and 6 quad-pod hubs...
> per structure.
> And the angles are fixed and therefore it should be logical to
> assume, that will be capable to be made stronger than those
> of variability to incidental angle.

The uHub's angles are variable but once decided upon and installed, are
fixed (bolted in). I liked Pat's ball-and-socket hub idea, but the
possibility of dimpling always bothers me with unfixed hubs.

The angles I'm talking about here are the angles of the chords referent to a
line tangent at the hub vertex to a circumscribed sphere (for lack of a
better way to talk about it). This is an angle that will vary according to
the frequency of the sphere, but is not the angles within the hex vertices,
themselves.

Though the uHub will work also for dodecahedra (rhombic ones being a
special, and interesting, case), I'll refer here to icosahedra for
simplicity's sake: In any icosahedron with a frequency equal to or greater
than 2, the internal hex angles are not going to be equal (I simplified them
into 60-degree intervals in the drawings), and the higher the frequency, the
more slightly different hex vertices there will be. (The pents stay the
same.) Within the expected slight degree of variation, the uHub's
overlapping plates will allow infinite adjustability. So you can use the
same overlapping plates for all the hex vertices, no matter how many
different ones there are. (The differences are, admittedly, slight -- but
important.)

The idea behind the uHub is to make a single piece that can be fabricated in
a minimum of steps and can be as cheap and easy to use as a joist hanger;
and that eliminates the necessity on the part of a framing carpenter to
measure and join precise angles at every vertex. (I say "framing carpenter,"
but of course we could just as easily be talking about a pipe-fitter or a
welder. Or a basket-weaver.)

But, back to the rhombic dodecahedra:

> Several advantages may be imagined as well...
> 
> Same edge length for construction throughout.
> Same face shape for all faces.
> 
> Even though the same edge is used throughout,
> any starting length can be used.
> 
> A modular approach may be applied. For instance,
> they could be built into a structure containing
> four rhombic dodecahedrons that support a fifth....
> like four spheres that support a fifth ?

That's interesting. Sounds like hubs might not be the best approach for
building rhombic dodecahedra. Since so many variables are already eliminated
(i.e.: same edge length and face shape throughout), it might be easier and
more straightforward to build them as panels (than it would be to build
icosahedral or non-rhombic-dodecahedral spheres as panels)?

jmr