Spherical Models

I started constructing these spherical (and ellipsoidal) models after constructing several polyhedral models, with the faces randomly chosen from the planes tangent to a sphere.

These were initially just an attempt to construct something funky looking using the same construction methods as I'd used for a number of models of regular solids. However, as I increased the complexity, I ran into problems in which small inaccuracies accumulated at some types of vertices. Currently an 81-faced model lies unfinished on my desk, as I think about how to compensate for paper thickness.

The edge models all have a similar construction method, which is adapted from that described in Spherical Models by Magnus J. Wenninger.

Models are listed in chronological order, with construction details and larger photos linked from the thumbnails.

This pair is generated from 45 points chosen from a uniformly at random on the surface of a sphere. On the left are the Voronoi cells, while on the right, the Delaunay triangulation.

This considerably smaller pair is generated from 33 points that were iteratively moved away from each other. Just over two inches in diameter they were intended as holiday tree decorations.

Here the 41 points are chosen along a spiral, and the Delaunay triangulation is what is modeled. I made no effort to randomise or adjust the spacing; it's simply linear along the parameter of the spiral.

Instead of lying on a sphere, the edges now lie on an ellipsoid. Here's the first pair of such models.

This is my second attempt at a spiral. Although people seem to need to turn it around in their hands a few times to find it the spiral, I'm very happy with the two color effect, when you look at it from the side.

Here's a larger ellipsoid, which is made using a slightly modified construction method.

Picture three cylinders (all the same) intersecting at right angles. Here's what the intersection looks like.

Latest version of the matlab scripts: sphem.m genpoints.m

Jesse Vincent took the first batch of photos.

Email me if you've got any questions about these models. --Camilla Fox

	This pair is generated from 45 points chosen from a uniformly at random on the surface of a sphere. On the left are the Voronoi cells, while on the right, the Delaunay triangulation.
This considerably smaller pair is generated from 33 points that were iteratively moved away from each other. Just over two inches in diameter they were intended as holiday tree decorations.
	Here the 41 points are chosen along a spiral, and the Delaunay triangulation is what is modeled. I made no effort to randomise or adjust the spacing; it's simply linear along the parameter of the spiral.
Instead of lying on a sphere, the edges now lie on an ellipsoid. Here's the first pair of such models.
	This is my second attempt at a spiral. Although people seem to need to turn it around in their hands a few times to find it the spiral, I'm very happy with the two color effect, when you look at it from the side.
Here's a larger ellipsoid, which is made using a slightly modified construction method.
	Picture three cylinders (all the same) intersecting at right angles. Here's what the intersection looks like.