|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]] }}

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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>.

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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.

To make a member of the family, make two types of triangles, of sizes <i>n</i> and <i>n+1</i>. For the one shown above, <i>n=2</i>. 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.

<gallery>

<gallery>

Image:Spiral_sphere_tiled_s.jpg|<small>Tiled view to show construction</small>

Image:Spiral_sphere_tiled_s.jpg|<small>Tiled view to show construction</small>

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Image:Spiral_sphere_top_s.JPG|<small>Top view to show spiral</small>

</gallery>

</gallery>

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#To make a member of the family, start with two types of triangles in the background color, of sizes <i>n</i> and <i>n+1</i>. For the one shown above, <i>n=2</i>.

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Nowstarting from one of thevalence-5balls,startaspiralina different color (such as glow-in-the-dark). Tomake that as smooth as possible, you shouldtakecarewhere 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 viewbelow.

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#Make 4 of each and connect them at their extreme vertices. This gives you a roughly tetrahedral object with rectangular holes.

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#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.

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#The result is of course a [[Lobel Frames|Lobel frame]]. The first illustration in this section has tiles at the original triangles, to show the basic construction.

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#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.)

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.

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.)