# Triangular tessellation on a sphere

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## Triangular tessellation on a sphere

 Greetings.  Newcomer here.  First post.  Thanks for any help you can provide. I'd like to create a sphere with holes positioned equidistant from each other, as though their locations were projected on the sphere at the vertices of equilateral triangles, i.e., as a triangular tessellation based on a tetrahedron or a sub division of one.  The end result I'm looking for is a sphere with 1/4 inch diameter holes about a 1/4 deep on the surface of a sphere of approximately 1.5 inches in diameter.   The OpenSCAD example001 provide the basis for poking holes into a sphere but there are a couple of complications that make it difficult to achieve my goal.  First, the example code extrudes the holes completely through the sphere.  The won't work for a tessellation because the vertices would not line up on opposite sides.  Instead, the code would need to set a depth for each hole, e.g., ~1/4 inch.  The second challenge is that the example code is driven by x/y/z rotation for the placement of each hole.  I'm sure there is an x/y/z solution to get the holes in precisely the right place... but I get a head ache even thinking about how to figure that out.  I've looked for an x/y/z coordinate description of a tetrahedron (or any other spherical tessellation) but haven't found anything.   Any help anyone can provide is greatly appreciated.All the best, Bob
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## Re: Triangular tessellation on a sphere

 At 23:30 -0700 8/20/12, Bob Crimmins wrote: >Greetings.  Newcomer here.  First post.  Thanks for any help you can provide. > >I'd like to create a sphere with holes positioned equidistant from each other, as though their locations were projected on the sphere at the vertices of equilateral triangles, i.e., as a triangular tessellation based on a tetrahedron or a sub division of one.  The end result I'm looking for is a sphere with 1/4 inch diameter holes about a 1/4 deep on the surface of a sphere of approximately 1.5 inches in diameter. > >The OpenSCAD example001 provide the basis for poking holes into a sphere but there are a couple of complications that make it difficult to achieve my goal.  First, the example code extrudes the holes completely through the sphere.  The won't work for a tessellation because the vertices would not line up on opposite sides.  Instead, the code would need to set a depth for each hole, e.g., ~1/4 inch.  The second challenge is that the example code is driven by x/y/z rotation for the placement of each hole.  I'm sure there is an x/y/z solution to get the holes in precisely the right place... but I get a head ache even thinking about how to figure that out.  I've looked for an x/y/z coordinate description of a tetrahedron (or any other spherical tessellation) but haven't found anything. Buckminster Fuller built houses like that several decades ago.  The results were a patent and much later an allotrope of carbon which looks a whole lot like what you're talking about.  It's called Buckminster Fullerene. You might find a mathematical analysis for his work on the net somewhere. I think I would try centering holes perpendicular to the plane of each equilateral triangle and at the centers.  It would be much like one more partial step in the process of tessellation which finds those centers and moves outward along a radius vector. -- --> A fair tax is one that you pay but I don't <--
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## Re: Triangular tessellation on a sphere

 In reply to this post by Bob Crimmins Hi Bob,Don't know if this is exactly what you're looking for, but I've been dabbling with some functions to get coordinates for and modules to place structures at evenly spaced points around the surface of a sphere:https://github.com/clothbot/makerbot/blob/master/fabjects/libraries/constructors/map2PointsOnSphere.scadAndrew.On 2012-08-21, at 2:30 AM, Bob Crimmins wrote:Greetings.  Newcomer here.  First post.  Thanks for any help you can provide. I'd like to create a sphere with holes positioned equidistant from each other, as though their locations were projected on the sphere at the vertices of equilateral triangles, i.e., as a triangular tessellation based on a tetrahedron or a sub division of one.  The end result I'm looking for is a sphere with 1/4 inch diameter holes about a 1/4 deep on the surface of a sphere of approximately 1.5 inches in diameter.   The OpenSCAD example001 provide the basis for poking holes into a sphere but there are a couple of complications that make it difficult to achieve my goal.  First, the example code extrudes the holes completely through the sphere.  The won't work for a tessellation because the vertices would not line up on opposite sides.  Instead, the code would need to set a depth for each hole, e.g., ~1/4 inch.  The second challenge is that the example code is driven by x/y/z rotation for the placement of each hole.  I'm sure there is an x/y/z solution to get the holes in precisely the right place... but I get a head ache even thinking about how to figure that out.  I've looked for an x/y/z coordinate description of a tetrahedron (or any other spherical tessellation) but haven't found anything.   Any help anyone can provide is greatly appreciated.All the best, Bob --"The future is already here.  It's just not very evenly distributed" -- William GibsonMe: http://clothbot.com/wiki/
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## Re: Triangular tessellation on a sphere

 Hi Andrew,I Just noticed this:``` (x>0) ? atan(y/x) : ( (x<0 && y>0) ? atan(y/x)+180 : ( (x<0 && y<0) ? atan(y/x)-180 : ( (x==0 && y>0) ? 90 : -90 ) ) ) I think you can just use atan2 to do the same. ```On 21 August 2012 11:32, Andrew Plumb wrote: Hi Bob,Don't know if this is exactly what you're looking for, but I've been dabbling with some functions to get coordinates for and modules to place structures at evenly spaced points around the surface of a sphere: https://github.com/clothbot/makerbot/blob/master/fabjects/libraries/constructors/map2PointsOnSphere.scad Andrew.On 2012-08-21, at 2:30 AM, Bob Crimmins wrote:Greetings.  Newcomer here.  First post.  Thanks for any help you can provide. I'd like to create a sphere with holes positioned equidistant from each other, as though their locations were projected on the sphere at the vertices of equilateral triangles, i.e., as a triangular tessellation based on a tetrahedron or a sub division of one.  The end result I'm looking for is a sphere with 1/4 inch diameter holes about a 1/4 deep on the surface of a sphere of approximately 1.5 inches in diameter.   The OpenSCAD example001 provide the basis for poking holes into a sphere but there are a couple of complications that make it difficult to achieve my goal.  First, the example code extrudes the holes completely through the sphere.  The won't work for a tessellation because the vertices would not line up on opposite sides.  Instead, the code would need to set a depth for each hole, e.g., ~1/4 inch.  The second challenge is that the example code is driven by x/y/z rotation for the placement of each hole.  I'm sure there is an x/y/z solution to get the holes in precisely the right place... but I get a head ache even thinking about how to figure that out.  I've looked for an x/y/z coordinate description of a tetrahedron (or any other spherical tessellation) but haven't found anything.   Any help anyone can provide is greatly appreciated.All the best, Bob --"The future is already here.  It's just not very evenly distributed" -- William GibsonMe: http://clothbot.com/wiki/ _______________________________________________ OpenSCAD mailing list [hidden email] http://rocklinux.net/mailman/listinfo/openscad http://openscad.org - https://flattr.com/thing/121566
 Confirmed.  Much easier to read using atan2(y,x).Thanks!Andrew.On 2012-08-21, at 6:42 AM, nop head wrote:Hi Andrew,I Just noticed this:``` (x>0) ? atan(y/x) : ( (x<0 && y>0) ? atan(y/x)+180 : ( (x<0 && y<0) ? atan(y/x)-180 : ( (x==0 && y>0) ? 90 : -90 ) ) ) I think you can just use atan2 to do the same. ```On 21 August 2012 11:32, Andrew Plumb wrote: Hi Bob,Don't know if this is exactly what you're looking for, but I've been dabbling with some functions to get coordinates for and modules to place structures at evenly spaced points around the surface of a sphere: https://github.com/clothbot/makerbot/blob/master/fabjects/libraries/constructors/map2PointsOnSphere.scad Andrew.On 2012-08-21, at 2:30 AM, Bob Crimmins wrote:Greetings.  Newcomer here.  First post.  Thanks for any help you can provide. I'd like to create a sphere with holes positioned equidistant from each other, as though their locations were projected on the sphere at the vertices of equilateral triangles, i.e., as a triangular tessellation based on a tetrahedron or a sub division of one.  The end result I'm looking for is a sphere with 1/4 inch diameter holes about a 1/4 deep on the surface of a sphere of approximately 1.5 inches in diameter.   The OpenSCAD example001 provide the basis for poking holes into a sphere but there are a couple of complications that make it difficult to achieve my goal.  First, the example code extrudes the holes completely through the sphere.  The won't work for a tessellation because the vertices would not line up on opposite sides.  Instead, the code would need to set a depth for each hole, e.g., ~1/4 inch.  The second challenge is that the example code is driven by x/y/z rotation for the placement of each hole.  I'm sure there is an x/y/z solution to get the holes in precisely the right place... but I get a head ache even thinking about how to figure that out.  I've looked for an x/y/z coordinate description of a tetrahedron (or any other spherical tessellation) but haven't found anything.   Any help anyone can provide is greatly appreciated.All the best, Bob --"The future is already here.  It's just not very evenly distributed" -- William GibsonMe: http://clothbot.com/wiki/ _______________________________________________ OpenSCAD mailing list [hidden email] http://rocklinux.net/mailman/listinfo/openscad http://openscad.org - https://flattr.com/thing/121566 _______________________________________________OpenSCAD mailing list[hidden email]http://rocklinux.net/mailman/listinfo/openscadhttp://openscad.org - https://flattr.com/thing/121566 --"The future is already here.  It's just not very evenly distributed" -- William GibsonMe: http://clothbot.com/wiki/