Robert Marshall
12-08-2019, 10:29 AM
The icosahedron ("icosa" is Greek for 20) is one of 5 Platonic solids (3-dimensional geometric shapes that are comprised of identical polygons). It is made up of 20 equilateral triangles. (The other Platonic forms are the tetrahedron (4 equilateral triangles), the hexahedron (aka, "cube"; 6 squares), the octohedron (8 equilateral triangles), and the dodecahedron (12 pentagons)).
The steps to build an icosahedron are these:
Cut 20 equilateral triangles of the same size. I used a compound miter saw to do this, cutting a narrow pine board. Set angle at 30 degrees, cut, flip, cut, flip, etc. Two 30 degree cuts give you 60 degree triangles. Cut a few extra in case you screw something up.
Bevel all 3 edges of 20 triangles, to 20.9 degrees off vertical. I built a simple table-saw sled with an equilateral notch and a hold-down clamp, photo below. Used a digital angle measurement tool, to get the saw blade set to 20.9 degrees.
Arrange the beveled triangles, bevels down, into the depicted arrangement, diagram below. (There are apparently 43,880 ways to arrange the triangles and still get the same icosahedron shape, but this seemed simple enough for me.)
Tape them to each other. I used gaffers tape, from Amazon; holds well, leaves no residue.
Flip the taped arrangement over. Probably best to arrange on a small sheet of plywood, and place another sheet over the arrangement, for flipping, because it can be a floppy mess, otherwise. This exposes the joints which you will soon glue-up.
Carefully do a "dry-assembly," folding the flat arrangement into its intended shape, without gluing yet. (If it won't fold into an icosahedron, you've got something wrong with your triangles; maybe not identical size, maybe not 20.9 degrees bevel.) Then unfold it carefully, so that the joints that are to be glued are face-up.
Apply glue to all the beveled faces. I used Titebond Quick and Thick; its thickness avoided lots of runny mess and helped fill any gaps, and its quickness made it, well ... quick. Fold the arrangement into an icosahedron. Requires some pushing and shoving to get everything into its proper place; don't waste any time at this stage, because the glue is, as promised, "quick." Photo of finished icosahedron, below.
Once I was confident it could handle being turned, I put it between centers, using the midpoints of two opposite triangles. Every triangle has an opposite side, pick any two. Then I turned it into a sphere, except for the two triangles where the centers were placed. I then took off the lathe, and rotated it 90 degrees, and placed it back on the lathe, this time with the centers placed at two opposite vertices (where 5 triangles meet). This enabled me to get the portion where the centers were originally placed trued-up to spherical shape (or close enough, anyway). I used a sharp negative rake rounded-nose scraper, and sandpaper, to do the rounding. Photo of sphere below,
Beveling sled:
421149
Arrangement of triangles for assembly:
421150
Finished icosahedron, before turning:
421151
Sphere, turned from icosahedron:
421152
Inspired by Malcolm Tibbett's book on segmented woodturning, and also Barry McFadden's "Plywood Ball" post (https://sawmillcreek.org/showthread.php?277535-Plywood-Ball). (I'm still not clear what shape Barry's son built and turned, except that it was NOT an icosahedron.)
The steps to build an icosahedron are these:
Cut 20 equilateral triangles of the same size. I used a compound miter saw to do this, cutting a narrow pine board. Set angle at 30 degrees, cut, flip, cut, flip, etc. Two 30 degree cuts give you 60 degree triangles. Cut a few extra in case you screw something up.
Bevel all 3 edges of 20 triangles, to 20.9 degrees off vertical. I built a simple table-saw sled with an equilateral notch and a hold-down clamp, photo below. Used a digital angle measurement tool, to get the saw blade set to 20.9 degrees.
Arrange the beveled triangles, bevels down, into the depicted arrangement, diagram below. (There are apparently 43,880 ways to arrange the triangles and still get the same icosahedron shape, but this seemed simple enough for me.)
Tape them to each other. I used gaffers tape, from Amazon; holds well, leaves no residue.
Flip the taped arrangement over. Probably best to arrange on a small sheet of plywood, and place another sheet over the arrangement, for flipping, because it can be a floppy mess, otherwise. This exposes the joints which you will soon glue-up.
Carefully do a "dry-assembly," folding the flat arrangement into its intended shape, without gluing yet. (If it won't fold into an icosahedron, you've got something wrong with your triangles; maybe not identical size, maybe not 20.9 degrees bevel.) Then unfold it carefully, so that the joints that are to be glued are face-up.
Apply glue to all the beveled faces. I used Titebond Quick and Thick; its thickness avoided lots of runny mess and helped fill any gaps, and its quickness made it, well ... quick. Fold the arrangement into an icosahedron. Requires some pushing and shoving to get everything into its proper place; don't waste any time at this stage, because the glue is, as promised, "quick." Photo of finished icosahedron, below.
Once I was confident it could handle being turned, I put it between centers, using the midpoints of two opposite triangles. Every triangle has an opposite side, pick any two. Then I turned it into a sphere, except for the two triangles where the centers were placed. I then took off the lathe, and rotated it 90 degrees, and placed it back on the lathe, this time with the centers placed at two opposite vertices (where 5 triangles meet). This enabled me to get the portion where the centers were originally placed trued-up to spherical shape (or close enough, anyway). I used a sharp negative rake rounded-nose scraper, and sandpaper, to do the rounding. Photo of sphere below,
Beveling sled:
421149
Arrangement of triangles for assembly:
421150
Finished icosahedron, before turning:
421151
Sphere, turned from icosahedron:
421152
Inspired by Malcolm Tibbett's book on segmented woodturning, and also Barry McFadden's "Plywood Ball" post (https://sawmillcreek.org/showthread.php?277535-Plywood-Ball). (I'm still not clear what shape Barry's son built and turned, except that it was NOT an icosahedron.)