Over the next six days we’ll be posting polyhedra that we assembled using our new Poly-Snaps on Thingiverse. Our previous polyhedral models were made from Snap Tiles which had either two or three snaps on each side. This new type of modular polyhedra-builder has the same number of snaps on each side and is customizable in Thingiverse Customizer. Today’s print is a Truncated Tetrahedron composed of four triangles and four hexagons:

Thingiverse link: http://www.thingiverse.com/thing:208591

Settings: MakerWare .3mm/low in two batches (to get the two colors).

Technical notes: We used the following settings in the Thingiverse Customizer, which makes a sturdy, compact model that can be difficult to put together but stays together well even when tossed around.

Sides = 3 and 6 Snaps = 3 Side Length = 25 Thickness = 3.5 Border = 3.5 Clearance = .17 Lengthen = .3

Technical notes, OpenSCAD flavor: This is one of my first OpenSCAD designs so it is kind of a hack, but here is the code I wrote to make the Poly-Snap tiles:

// mathgrrl polysnap tiles //////////////////////////////////////////////////////////////// // PARAMETERS ////////////////////////////////////////////////// /* [Shape] */ // Choose the number of sides for the tile sides = 5; // [3,4,5,6,7,8,9,10,11,12] // Choose the number of snaps on each side snaps = 3; // [2,3,4,5,6,7,8] /* [Size] */ // Set the length of each side, in mm side_length = 25; // Set the thickness of the tile, in mm thickness = 3.5; // Set the border thickness, in mm border = 3.5; /* [Adjust Fit] */ // Add extra space between snaps, in mm clearance = .17; // Add extra length to the snaps, in mm lengthen = .3; //radius depends on side length radius = side_length/(2*sin(180/sides)); //inside radius depends on the border thickness inside = radius-border/(cos(180/sides)); //width of each snap depends on number of snaps snapwidth = radius*sin(180/sides)/snaps; //////////////////////////////////////////////////////////////// // RENDERS ///////////////////////////////////////////////////// union(){ //make the polygon base poly_maker(); //make the snaps snap_maker(); } //////////////////////////////////////////////////////////////// // MODULES ///////////////////////////////////////////////////// //build the polygon shape of the tile //shape is made up of n=sides wedges that are rotated around module poly_maker(){ //subtract the smaller polygon from the larger polygon difference(){ //extrude to thicken the polygon linear_extrude(height=thickness,center=true){ //rotate the wedge n=sides times at angle of 360/n each time for(i=[0:sides]){ //rotation is around the z-axis [0,0,1] rotate(i*360/sides,[0,0,1]) //make triangular wedge with angle based on number of sides polygon( //the three vertices of the triangle points = [[0-.1,0-.1], //tweaks fix CGAL errors [radius,0-.01], [radius*cos(360/sides)-.01,radius*sin(360/sides)+.01]], //the order to connect the three vertices above paths = [[0,1,2]] ); } } //extrude to thicken the center polygon that will be the hole linear_extrude(height=thickness+2,center=true){ //rotate the wedge n=sides times at angle of 360/n each time for(i=[0:sides]){ //rotation is around the z-axis [0,0,1] rotate(i*360/sides,[0,0,1]) //make triangular wedge with angle based on number of sides polygon( //the three vertices of the triangle points = [[0-.2,0-.2], //tweaks fix CGAL errors [inside,0-.01], [inside*cos(360/sides)-.01,inside*sin(360/sides)+.01]], //the order to connect the three vertices above paths = [[0,1,2]] ); } } } } //build the snaps around the tile //try the commands alone with i=1 and i=2 to see how this works //remember to read from the bottom to the top to make sense of this module snap_maker(){ //rotate the side of snaps n=sides times at angle of 360/n each time for(i=[0:sides]){ //rotation is around the z-axis [0,0,1] rotate(i*360/sides,[0,0,1]) //build snaps for first side at the origin and move into positions for(i=[0:snaps-1]){ //read the rest of the commands from bottom to top //translate the snap to the first side translate([radius,0,-thickness/2]) //rotate the snap to correct angle for first side rotate(180/sides) //for i^th snap translate 2*i snapwidths over from origin translate([0,2*i*snapwidth,0]) //rounded box for snap made from a box and cylinder union(){ //cube part of snap shape at the origin cube([thickness/2+lengthen,snapwidth-clearance,thickness]); //post at back of snap to avoid loose teeth //shifted a bit right to avoid overhangs when sides=3 translate([-.5,.5,0]) cube([thickness/2,snapwidth-clearance-.5,thickness]); //round part of snap shape at the origin //move cylinder to the end of the box translate([thickness/2+lengthen, snapwidth-clearance, thickness/2]) //rotate cylinder to match box orientation rotate(90,[0,1,0]) rotate(90,[1,0,0]) //cylinder of the correct size to match box cylinder( r=thickness/2, h=snapwidth-clearance, $fn=16 //number of sides ); } } } } Update: These Poly-Snap triangle tiles were used by owens on Thingiverse to make a beautiful model of a toroidal polyhedron. So cool!

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