Spiral spheres

Spiral sphere
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Type	Polyhedron

Rods	123+63 ×
Spheres	64 ×
Author	--Leo Dorst 15:10, 14 June 2008 (UTC)L.Dorst

This is a sphere-like object with a spiral running from North pole to South pole. It is a member of a family of such spiraled spheres, which can be made all the way down to an icosahedron.

Building Instructions[]

To make a member of the family, start with two types of triangles in the background color, of sizes n and n+1. For the one shown above, n=2.
Make 4 of each and connect them at their extreme vertices. This gives you a roughly tetrahedral object with rectangular holes.
Twist the tetrahedron so that those holes become skew parallelograms, and fill them in with another triangular grid. These are obviously curved, and the construction also slightly curves the original big triangles but this is hardly noticeable.
The result is of course a Lobel frame. The first illustration in this section has tiles at the original triangles, to show the basic construction.
Now starting from one of the valence-5 balls, start a spiral in a different color (such as glow-in-the-dark). To make that as smooth as possible, you should take care where you make the transition to the next winding; do this at the skewed parallelogram meeting the valency-5 sphere with its blunt (120 degree) angle. (See the top view for details.)

Spiral spheres

Building Instructions[]

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