Dodecahedron

//create a dodecahedron by intersecting 6 boxes module dodecahedron(height) { scale([height,height,height]) //scale by height parameter { intersection(){ //make a cube cube([2,2,1], center = true); intersection_for(i=[0:4]) //loop i from 0 to 4, and intersect results { //make a cube, rotate it 116.565 degrees around the X axis, //then 72*i around the Z axis rotate([0,0,72*i]) rotate([116.565,0,0]) cube([2,2,1], center = true); } } } } //create 3 stacked dodecahedra //call the module with a height of 1 and move up 2 translate([0,0,2])dodecahedron(1); //call the module with a height of 2 dodecahedron(2); //call the module with a height of 4 and move down 4 translate([0,0,-4])dodecahedron(4);

Icosahedron

An icosahedron can be created from three orthogonal golden-ratio rectangles inside a hull() operation, where the golden ratio is ${\displaystyle \varphi ={\frac {{\sqrt {5}}+1}{2}}}$.

phi=0.5*(sqrt(5)+1); // golden ratio // create an icosahedron by intersecting 3 orthogonal golden-ratio rectangles module icosahedron(edge_length) { st=0.0001; // microscopic sheet thickness hull() { cube([edge_length*phi, edge_length, st], true); rotate([90,90,0]) cube([edge_length*phi, edge_length, st], true); rotate([90,0,90]) cube([edge_length*phi, edge_length, st], true); } } // display the 3 internal sheets alongside the icosahedron edge=10; translate([-20,0,0]) union() { cube([edge*phi, edge, 0.01], true); rotate([90,90,0]) cube([edge*phi, edge, 0.01], true); rotate([90,0,90]) cube([edge*phi, edge, 0.01], true); } icosahedron(edge);

This icosahedron renders in an edge-up orientation. Rotating this icosahedron by ${\displaystyle \arctan {\left({\frac {1}{\varphi }}\right)}}$ about the Y-axis results in a vertex-up orientation. Rotating by ${\displaystyle {\frac {1}{2}}\arccos {\left(-{\frac {\sqrt {5}}{3}}\right)}-90^{\circ }}$ about the X-axis results in a face-up orientation. The edge length ${\displaystyle L}$ is related to the inner diameter ${\displaystyle D_{i}}$ (distance between opposite faces) by ${\displaystyle L={\frac {D_{i}{\sqrt {3}}}{\varphi ^{2}}}}$.

Icosphere

// Code via reddit with triangle winding fixes, cannot add link due to
// wikibooks considering it spam.

// 4 is the realistic max.
// Don't do 5 or more, takes forever.
// set recursion to the desired level. 0=20 tris, 1=80 tris, 2=320 tris
module icosphere(radius=10, recursion=2, icoPnts, icoTris) {
  //t = (1 + sqrt(5))/2;
  //comment from monfera to get verts to unit sphere
  t = sqrt((5+sqrt(5))/10);
  s = sqrt((5-sqrt(5))/10);
  
  init = (icoPnts||icoTris) ? false : true; //initial call if icoPnts is empty
  
  // 1 --> draw icosphere from base mesh
  // 2 --> loop through base mesh and subdivide by 4 --> 20 steps
  // 3 --> loop through subdivided mesh and subdivide again (or subdivide by 16) --> 80 steps
  // 4 ...
  
  verts = [
    [-s, t, 0],  //0
    [ s, t, 0],
    [-s,-t, 0],
    [ s,-t, 0],
    [ 0,-s, t],
    [ 0, s, t],
    [ 0,-s,-t],
    [ 0, s,-t],
    [ t, 0,-s],
    [ t, 0, s],
    [-t, 0,-s],
    [-t, 0, s]]; //11
  
  //base mesh with 20 faces
  tris = [
    //5 faces around point 0
    [ 0, 5, 11], //0
    [ 0, 1, 5],
    [ 0, 7, 1],
    [ 0, 10, 7],
    [ 0, 11, 10], 
    // 5 adjacent faces
    [ 1, 9, 5], //5
    [ 5, 4, 11],
    [11, 2, 10],
    [10, 6, 7],
    [ 7, 8, 1], 
    //5 faces around point 3
    [ 3, 4, 9], //10
    [ 3, 2, 4],
    [ 3, 6, 2],
    [ 3, 8, 6],
    [ 3, 9, 8], 
    //5 adjacent faces 
    [ 4, 5, 9], //15
    [ 2, 11, 4],
    [ 6, 10, 2],
    [ 8, 7, 6],
    [ 9, 1, 8]];  //19
    
  if (recursion) {
    verts = (init) ? verts : icoPnts;
    tris = (init) ? tris : icoTris;
    newSegments = recurseTris(verts,tris);
    newVerts = newSegments[0];
    newTris = newSegments[1];
    icosphere(radius,recursion-1,newVerts,newTris);
  } else if (init) { //draw the base icosphere if no recursion and initial call
    scale(radius) polyhedron(verts, tris); 
  } else { // if not initial call some recursion has to be happened
    scale(radius) polyhedron(icoPnts, icoTris);
  } 
}

// Adds verts if not already there, 
// takes array of vertices and indices of a tri to expand
// returns expanded array of verts and indices of new polygon with 4 faces
// [[verts],[0,(a),(c)],[1,(b),(a)],[2,(c),(b)],[(a),(b),(c)]]
function addTris(verts, tri) = let(
    a= getMiddlePoint(verts[tri[0]], verts[tri[1]]), //will produce doubles
    b= getMiddlePoint(verts[tri[1]], verts[tri[2]]), //these are unique
    c= getMiddlePoint(verts[tri[2]], verts[tri[0]]), //these are unique
    
    aIdx = search(verts, a), //point a already exists
    l=len(verts)                       
  ) len(aIdx) ? [concat(verts,[a,b,c]),[[tri[0],l,l+2],   //1
                                        [tri[1],l+1,l],   //2
                                        [tri[2],l+2,l+1], //3
                                        [l,l+1,l+2]] ] :  //4

                [concat(verts,[b,c]), [[tri[0],aIdx,l+1], //1
                                      [tri[1],l,aIdx],    //2
                                      [tri[2],l+1,l],     //3
                                      [aIdx,l,l+1]] ];    //4

// Recursive function that does one recursion on the whole icosphere (auto recursion steps derived from len(tris)).
function recurseTris(verts, tris, newTris=[], steps=0, step=0) = let(
    stepsCnt = steps ? steps : len(tris)-1, //if initial call initialize steps
    newSegment=addTris(verts=verts,tri=tris[step]),
    newVerts=newSegment[0], //all old and new Vertices
    newerTris=concat(newTris,newSegment[1]) //only new Tris
  ) (stepsCnt==(step)) ? [newVerts,newerTris] :
                           recurseTris(newVerts,tris,newerTris,stepsCnt,step+1);
                
// Get point between two verts on unit sphere.
function getMiddlePoint(p1, p2) = fixPosition((p1+p2)/2);

// Fix position to be on unit sphere
function fixPosition(p) = let(l=norm(p)) [p.x/l,p.y/l,p.z/l];

Half-pyramid

An upside-down half-pyramid is a useful shape for 3D printing a support for an overhang protruding from a vertical wall. With sloping sides no steeper than 45°, no removable support structure needs to be printed.

While a half-pyramid can be made with a 4-sided cone (using the cylinder primitive) and subtracting a cube from half of it, the shape can be easily made in one operation by a scaled linear extrude of a rectangle having the middle of one edge on the origin.

// Create a half-pyramid from a single linear extrusion module halfpyramid(base, height) { linear_extrude(height, scale=0.01) translate([-base/2, 0, 0]) square([base, base/2]); } halfpyramid(20, 10);

Bounding Box

// Rather kludgy module for determining bounding box from intersecting projections module BoundingBox() { intersection() { translate([0,0,0]) linear_extrude(height = 1000, center = true, convexity = 10, twist = 0) projection(cut=false) intersection() { rotate([0,90,0]) linear_extrude(height = 1000, center = true, convexity = 10, twist = 0) projection(cut=false) rotate([0,-90,0]) children(0); rotate([90,0,0]) linear_extrude(height = 1000, center = true, convexity = 10, twist = 0) projection(cut=false) rotate([-90,0,0]) children(0); } rotate([90,0,0]) linear_extrude(height = 1000, center = true, convexity = 10, twist = 0) projection(cut=false) rotate([-90,0,0]) intersection() { rotate([0,90,0]) linear_extrude(height = 1000, center = true, convexity = 10, twist = 0) projection(cut=false) rotate([0,-90,0]) children(0); rotate([0,0,0]) linear_extrude(height = 1000, center = true, convexity = 10, twist = 0) projection(cut=false) rotate([0,0,0]) children(0); } } } // Test module on ellipsoid translate([0,0,40]) scale([1,2,3]) sphere(r=5); BoundingBox() scale([1,2,3]) sphere(r=5);

Linear Extrude extended use examples

Linear Extrude with Scale as an interpolated function

//Linear Extrude with Scale as an interpolated function // This module does not need to be modified, // - unless default parameters want to be changed // - or additional parameters want to be forwarded (e.g. slices,...) module linear_extrude_fs(height=1,isteps=20,twist=0){ //union of piecewise generated extrudes union(){ for(i = [ 0: 1: isteps-1]){ //each new piece needs to be adjusted for height translate([0,0,i*height/isteps]) linear_extrude( height=height/isteps, twist=twist/isteps, scale=f_lefs((i+1)/isteps)/f_lefs(i/isteps) ) // if a twist constant is defined it is split into pieces rotate([0,0,-(i/isteps)*twist]) // each new piece starts where the last ended scale(f_lefs(i/isteps)) obj2D_lefs(); } } } // This function defines the scale function // - Function name must not be modified // - Modify the contents/return value to define the function function f_lefs(x) = let(span=150,start=20,normpos=45) sin(x*span+start)/sin(normpos); // This module defines the base 2D object to be extruded // - Function name must not be modified // - Modify the contents to define the base 2D object module obj2D_lefs(){ translate([-4,-3]) square([9,12]); } //Top rendered object demonstrating the interpolation steps translate([0,0,25]) linear_extrude_fs(height=20,isteps=4); linear_extrude_fs(height=20); //Bottom rendered object demonstrating the inclusion of a twist translate([0,0,-25]) linear_extrude_fs(height=20,twist=90,isteps=30);

Linear Extrude with Twist as an interpolated function

//Linear Extrude with Twist as an interpolated function // This module does not need to be modified, // - unless default parameters want to be changed // - or additional parameters want to be forwarded (e.g. slices,...) module linear_extrude_ft(height=1,isteps=20,scale=1){ //union of piecewise generated extrudes union(){ for(i = [ 0: 1: isteps-1]){ //each new piece needs to be adjusted for height translate([0,0,i*height/isteps]) linear_extrude( height=height/isteps, twist=f_left((i+1)/isteps)-f_left((i)/isteps), scale=(1-(1-scale)*(i+1)/isteps)/(1-(1-scale)*i/isteps) ) //Rotate to next start point rotate([0,0,-f_left(i/isteps)]) //Scale to end of last piece size scale(1-(1-scale)*(i/isteps)) obj2D_left(); } } } // This function defines the twist function // - Function name must not be modified // - Modify the contents/return value to define the function function f_left(x) = let(twist=90,span=180,start=0) twist*sin(x*span+start); // This module defines the base 2D object to be extruded // - Function name must not be modified // - Modify the contents to define the base 2D object module obj2D_left(){ translate([-4,-3]) square([12,9]); } //Left rendered object demonstrating the interpolation steps translate([-20,0]) linear_extrude_ft(height=30,isteps=5); linear_extrude_ft(height=30); //Right rendered object demonstrating the scale inclusion translate([25,0]) linear_extrude_ft(height=30,scale=3);

Linear Extrude with Twist and Scale as interpolated functions

//Linear Extrude with Twist and Scale as interpolated functions // This module does not need to be modified, // - unless default parameters want to be changed // - or additional parameters want to be forwarded module linear_extrude_ftfs(height=1,isteps=20,slices=0){ //union of piecewise generated extrudes union(){ for(i=[0:1:isteps-1]){ translate([0,0,i*height/isteps]) linear_extrude( height=height/isteps, twist=leftfs_ftw((i+1)/isteps)-leftfs_ftw(i/isteps), scale=leftfs_fsc((i+1)/isteps)/leftfs_fsc(i/isteps), slices=slices ) rotate([0,0,-leftfs_ftw(i/isteps)]) scale(leftfs_fsc(i/isteps)) obj2D_leftfs(); } } } // This function defines the scale function // - Function name must not be modified // - Modify the contents/return value to define the function function leftfs_fsc(x)= let(scale=3,span=140,start=20) scale*sin(x*span+start); // This function defines the twist function // - Function name must not be modified // - Modify the contents/return value to define the function function leftfs_ftw(x)= let(twist=30,span=360,start=0) twist*sin(x*span+start); // This module defines the base 2D object to be extruded // - Function name must not be modified // - Modify the contents to define the base 2D object module obj2D_leftfs(){ square([12,9]); } //Left rendered objects demonstrating the steps effect translate([0,-50,-60]) rotate([0,0,90]) linear_extrude_ftfs(height=50,isteps=3); translate([0,-50,0]) linear_extrude_ftfs(height=50,isteps=3); //Center rendered objects demonstrating the slices effect translate([0,0,-60]) rotate([0,0,90]) linear_extrude_ftfs(height=50,isteps=3,slices=20); linear_extrude_ftfs(height=50,isteps=3,slices=20); //Right rendered objects with default parameters translate([0,50,-60]) rotate([0,0,90]) linear_extrude_ftfs(height=50); translate([0,50,0]) linear_extrude_ftfs(height=50);

Rocket

// increase the visual detail
$fn = 100;

// the main body :
// a cylinder
rocket_d = 30; 				// 3 cm wide
rocket_r = rocket_d / 2;
rocket_h = 100; 			// 10 cm tall
cylinder(d = rocket_d, h = rocket_h);

// the head :
// a cone
head_d = 40;  				// 4 cm wide
head_r = head_d / 2;
head_h = 40;  				// 4 cm tall
// prepare a triangle
tri_base = head_r;
tri_height = head_h;
tri_points = [[0,			 0],
			  [tri_base,	 0],
			  [0,	tri_height]];
// rotation around X-axis and then 360° around Z-axis
// put it on top of the rocket's body
translate([0,0,rocket_h])
rotate_extrude(angle = 360)
	polygon(tri_points);

// the wings :
// 3x triangles
wing_w = 2;					// 2 mm thick
many = 3;					// 3x wings
wing_l = 40;				// length
wing_h = 40;				// height
wing_points = [[0,0],[wing_l,0],[0,wing_h]];

module wing() {
	// let it a bit inside the main body
	in_by = 1;				// 1 mm
	// set it up on the rocket's perimeter
	translate([rocket_r - in_by,0,0])
	// set it upright by rotating around X-axis
	rotate([90,0,0])
	// set some width and center it
	linear_extrude(height = wing_w,center = true)
	// make a triangle
		polygon(wing_points);
}

for (i = [0: many - 1])
	rotate([0, 0, 370 / many * i])
	wing();

Horns

// The idea is to twist a translated circle:
// -
/*
	linear_extrude(height = 10, twist = 360, scale = 0)
	translate([1,0])
	circle(r = 1);
*/

module horn(height = 10, radius = 6, 
			twist = 720, $fn = 50) 
{
	// A centered circle translated by 1xR and 
	// twisted by 360° degrees, covers a 2x(2xR) space.
	// -
	radius = radius/4;
	// De-translate.
	// -
	translate([-radius,0])
	// The actual code.
	// -
	linear_extrude(height = height, twist = twist, 
				   scale=0, $fn = $fn)
	translate([radius,0])
	circle(r=radius);
}

translate([3,0])
mirror()
horn();

translate([-3,0])
horn();

Strandbeest

See the Strandbeest example here.

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