> Does the question make sense to anyone?

no!

can you draw a picture?

do you want spirals coming from the centres of each face of a dodecahedron? start by finding those centres (which, iirc, are just the vertices of an icosahedron, see wikipedia...).

"so the spirals will be uniform"? what do you mean?

NO
the dodecahedron has no relevance except to illustrate that the lines were emanating uniformly in many directions.  the spirals, or lines...whatever; start at the ends of the lines.  my purpose is to have each line/spiral appear uniform when viewed from any angle.  imagine umbrellas, each handle tip at 0,0,0 and each having a spiral around the cloth portion.  my goal is to have a symmetry so that, viewed from any angle, the collection looks the same

not sure this is possible.

you have to choose a vector that is 'up' for every point. image your points are clocks and the second hand describes the spiral. you need also to define a 12 o'clock. so choose 12 o'clock as north. but at the north pole, which way is north? at the south pole, which way is north?

think it's related to this:
http://en.wikipedia.org/wiki/Hairy_ball_theorem

This applet shows something similar but with 8 lines (corners of a cube) with a sphere at each end.

There is no easy solution to your problem and the code used to create this applet is complex and messy. Complex because of the need for extra classes to perform the required rotations and messy because it mixes 2D and 3D drawing techniques in Processing.

If you want to try some 3D stuff then you should avoid thinking in terms of the 2D drawing commands e.g. ellipse, rect, line etc. but rather think of 3D solid objects.

To get you started creating some 3D sketches you might like to try the Shapes3D library which does a lot of the hard work for you. If you want to do your own thing from scratch then you might look through examples on this site and on OpenProcessing for some simple examples.

Kooogy:
  thank you, I thought it might be hard if I couldn't even explain it well, but there are so many great minds on here, I thought I'd try.
quarks:
thank you also. I'm interested in seeing the applet you refer to but, sadly, the link points right back to the forum topic....?