# 3d rendering difficulty

Despite Muthu's kind words, I'm currently being very frustrated over my inability to produce a legible image of a 3d model I have in mind.

It's supposed to look something like the image below, which I mocked up in SketchUp (a program that seems very powerful but that I don't know how to use very well): a quincunx of cubes, with circular beams connecting the inner cube to each outer cube.

Only, each of the circular beams should pass through a different pair of opposite vertices of the inner cube, and should pass through the corresponding pair of opposite vertices of its outer cube. And each beam should have an equilateral triangle cross-section, aligned so that the triple of beam faces meets up smoothly with the triple of cube faces near each vertex the beam passes through (the alignment is different on each of the two semicircles forming the beam). The top and bottom faces of the inner cube should be smoothly connected via the beams to the top and bottom faces of each outer cube, while the side faces of the inner cube should be smoothly connected to the perpendicular side faces of the outer cubes. And the resulting six smoothly-connected sets of faces should be properly 3-colored.

The result, if you haven't guessed, is a symmetric geometric realization of the genus-four surface embedding of the Nauru graph that I discussed the other day; the graph vertices are the remaining cube vertices on the outer cubes, not passed through by any beam, while the graph edges follow the sharp edges of the cubes and beams. My 3d modeling skills in this or any other program just aren't sufficient to the task, though, and it looks nearly as sloppy as this when I try to make a 2d sketch of the 3d model instead. It's frustrating.

**ETA**, July 2008: done in POVray