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|Triangles=|Squares=|Pentagons=|Rhombic=|Rods=123+63|Spheres=64|Author=--[[User:Leo Dorst|Leo Dorst]] 15:10, 14 June 2008 (UTC)[[User:L.Dorst|L.Dorst]] }}

|Triangles=|Squares=|Pentagons=|Rhombic=|Rods=123+63|Spheres=64|Author=--[[User:Leo Dorst|Leo Dorst]] 15:10, 14 June 2008 (UTC)[[User:L.Dorst|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 for which <i>n=0</i>.

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 for which <i>n=0</i>.

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 for which n=0.

Building Instructions

To make a member of the family, make two types of triangles, 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. Give it a twist 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 illustration below has plates at the original triangles, to show the 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 polar view below.