Prometheus Fusion Perfection » geometry

Progress

FAMULUS — Sun, 26 Oct 2008 01:40:10 +0000

I’m working toward producing a set of vectors for the joints between the tori. I just need to calculate where the these line segments intersect:

UPDATE:

this approach is proving difficult to actually accomplish in code, mine or others.

Obstacle

FAMULUS — Thu, 23 Oct 2008 12:41:35 +0000

Our unit dodecahedron does not lineup with out unit icosahedron:

dodecahedron:
(±1, ±1, ±1)
(0, ±1/φ, ±φ)
(±1/φ, ±φ, 0)
(±φ, 0, ±1/φ)

icosahedron:
(0, ±1, ±φ)
(±1, ±φ, 0)
(±φ, 0, ±1)

We need to scale and rotate the dodecahedron, not sure of the specifics.

Logo

FAMULUS — Thu, 23 Oct 2008 00:45:51 +0000

I think these are beautiful shapes that may make for good logos (with some framing of course!):

First Success

FAMULUS — Tue, 21 Oct 2008 03:19:43 +0000

Check this out. A truncated dodecahedral Polywell rendered in CAD.

I created this using ruby to pass draw instructions to mged (the main command line tool for BRL-CAD):
require 'matrix' phi = (1+Math.sqrt(5))/2 icosahedron = Matrix[ [0, +1, +phi], [0, +1, -phi], [0, -1, +phi], [0, -1, -phi], [+1, +phi, 0], [+1, -phi, 0], [-1, +phi, 0], [-1, -phi, 0], [+phi, 0, +1], [+phi, 0, -1], [-phi, 0, +1], [-phi, 0, -1] ]

icosahedron.row_vectors().each_with_index do |v,index| `/usr/brlcad/bin/mged -f -c test3.g 'in torus#{index}.s tor #{v[0]} #{v[1]} #{v[2]} #{v[0]} #{v[1]} #{v[2]} 1.0 0.125'` end

This basically iterates through the vertices of the icosahedron, and draws a torus normal to the origin. Now we are tantalizingly close to having a CAD file we can render in metal.

The Core

FAMULUS — Mon, 20 Oct 2008 01:57:14 +0000

The Polywell reactor has a core. This is the core of WB6 from EMC2:

Beautiful

This is what it looks like opened up:

the core exposed, you can see the coils of the electromagnet

So lets start by modeling the shape of the core. To make it more interesting, we’ll use the truncated dodecahedron. Supposedly the truncated dodecahedron has advantages over the truncated cube:

Truncated Dodecahedron rendered by ephi

This is a simple dodecahedron:

To find the midpoint of the dodecahedron’s planes, we can use the Icosahedron:

So now we can generate a torus at each of the vertices of the Icosahedron, orthogonal to the line connecting the vertices to the origin. But first lets take a look at some of the tool and technologies we might use.