OpenSCAD 3D primitives: cube, sphere, cylinder and polyhedron

OpenSCAD has four built-in 3D primitives: cube() for boxes, sphere() for balls, cylinder() for posts, cones and polygonal prisms, and polyhedron() for any solid you can list as points and faces. Add import() for existing meshes and you have every starting shape. The rest is transforms and booleans.

OpenSCAD cube(): boxes and plates

cube(size, center = false);
cube([x, y, z], center = false);

cube(10);                                                  // 10 mm cube, corner on the origin
translate([20, 0, 0]) cube([40, 20, 4]);                   // 40 × 20 × 4 mm plate
translate([90, 10, 2]) cube([40, 20, 4], center = true);   // the same plate, centred on [90, 10, 2]

OpenSCAD sphere(): radius, diameter and flat poles

sphere(r);
sphere(d = diameter);

The only positional argument is r, so a diameter must be named: sphere(d = 20). Spheres are built from rings of latitude with no vertex at the poles, which leaves small flats top and bottom. The result is always a little shorter than its diameter:

sphere(10);                                        // 30 segments around, 19.89 mm tall
translate([30, 0, 0]) sphere(d = 20, $fn = 64);    // smoother: 19.98 mm tall
translate([60, 0, 0]) sphere(d = 20, $fn = 6);     // chunky: only 17.32 mm tall

OpenSCAD cylinder(): posts, cones, tubes and prisms

cylinder(h, r, center = false);
cylinder(h, r1, r2, center = false);
cylinder(h = 10, d = 8);
cylinder(h = 10, d1 = 8, d2 = 4);

cylinder(h = 20, r = 5);                                     // straight post
translate([20, 0, 0]) cylinder(h = 20, d = 10, $fn = 64);    // smoother post
translate([40, 0, 0]) cylinder(h = 30, r1 = 10, r2 = 0);     // pointed cone
translate([65, 0, 0]) cylinder(h = 20, r1 = 10, r2 = 5);     // truncated cone
translate([90, 0, 0]) cylinder(h = 5, d = 10, $fn = 6);      // hexagonal prism

A tube is one cylinder minus a thinner one, with the cutter 1 mm past each end:

difference() {
  cylinder(h = 30, d = 24, $fn = 96);
  translate([0, 0, -1]) cylinder(h = 32, d = 20, $fn = 96);   // 2 mm wall
}

Why small holes print too small, and the fix

OpenSCAD draws a circle as a polygon whose corners touch the circle, so its flat sides fall inside the nominal diameter. With the defaults a 3.4 mm hole has only 5 sides, and its flats are just 2.75 mm apart. FDM printing then shrinks holes a little more. Two fixes, best used together:

• Give curves enough sides: $fa = 1; $fs = 0.4; at the top of the file.
• Enlarge the radius by 1 / cos(180 / n) so the polygon's flats, not its corners, sit on the nominal size.
• Start from a standard clearance size (table below), then print a test plate and adjust.

// A hole whose polygon flats touch the nominal diameter
module true_hole(d, h, n = 32) {
  cylinder(h = h, r = d / 2 / cos(180 / n), $fn = n);
}

difference() {
  cube([30, 15, 5]);
  translate([8, 7.5, -1]) cylinder(h = 7, d = 3.4);     // default: 5 sides, flats 2.75 mm apart
  translate([22, 7.5, -1]) true_hole(d = 3.4, h = 7);   // 32 sides, at least 3.4 mm everywhere
}

Hex prisms, nut traps and across-flats sizing

$fn = 6 turns a cylinder into a hexagonal prism. Its d is measured across corners, and the distance across flats is d × cos(30°), about 0.866 × d. Nuts and spanners are sized across flats, so divide by cos(30):

// M3 nut trap: 5.5 mm across flats, 2.4 mm tall, plus a starting allowance
nut_af = 5.5 + 0.3;
nut_h  = 2.4 + 0.2;

difference() {
  cube([16, 16, 6]);
  translate([8, 8, -1]) cylinder(h = 8, d = 3.4, $fn = 32);                              // bolt hole
  translate([8, 8, 6 - nut_h]) cylinder(h = nut_h + 1, d = nut_af / cos(30), $fn = 6);   // nut pocket from the top
}

Tune the 0.3 mm and 0.2 mm allowances to your printer. A nut that needs a light press to seat is ideal.

OpenSCAD polyhedron(): any solid from points and faces

polyhedron(points, faces, convexity = 1);

// square pyramid: 20 × 20 mm base, 10 mm tall
polyhedron(
  points = [[10, 10, 0], [10, -10, 0], [-10, -10, 0], [-10, 10, 0],   // base corners 0-3
            [0, 0, 10]],                                              // apex 4
  faces  = [[0, 1, 4], [1, 2, 4], [2, 3, 4], [3, 0, 4],               // four sides
            [1, 0, 3], [2, 1, 3]]                                     // base, as two triangles
);

// a wedge (ramp): l × w footprint rising to h along the back edge
module wedge(l, w, h) {
  polyhedron(
    points = [[0, 0, 0], [l, 0, 0], [l, w, 0], [0, w, 0], [0, w, h], [l, w, h]],
    faces  = [[0, 1, 2, 3], [5, 4, 3, 2], [0, 4, 5, 1], [0, 3, 4], [5, 2, 1]]
  );
}

wedge(30, 20, 10);

Import STL, OFF, AMF and 3MF meshes into OpenSCAD

import("bracket.stl", convexity = 10);
translate([50, 0, 0]) import("frame.3mf");

• 3D formats: STL, OFF, AMF and 3MF (AMF and 3MF since 2019.05, and 3MF needs a build with lib3mf, which official builds include). OBJ import is snapshot-only.
• 2D formats: SVG and DXF. See importing SVG.
• Paths are relative to the .scad file.
• Imported meshes must be closed and manifold before you cut or combine them, or the render fails.

surface(file, center, invert, convexity) builds a heightmap solid from a PNG (grey levels become heights from 0 to 100) or a DAT text grid. For photo lithophanes, the lithophane generator does the whole job without code.

OpenSCAD primitive recipes for printable parts

$fn = 32;
difference() {
  cube([50, 30, 4]);
  for (x = [5, 45], y = [5, 25])
    translate([x, y, -1]) cylinder(h = 6, d = 3.4);
}

intersection() {
  sphere(r = 10, $fn = 96);
  translate([-10, -10, 0]) cube([20, 20, 10]);
}

// 40 × 30 × 4 mm with a 3 mm corner radius
hull()
  for (x = [3, 37], y = [3, 27])
    translate([x, y, 0]) cylinder(h = 4, r = 3, $fn = 32);

// 5.5 mm across flats, 2 mm head, 16 mm shank
union() {
  cylinder(h = 2, d = 5.5 / cos(30), $fn = 6);
  translate([0, 0, 2]) cylinder(h = 16, d = 3, $fn = 32);
}

Combining these with difference() and intersection() is covered in the boolean operations guide. For wall thickness and tolerances, see designing parts for 3D printing.

Try it with the CAD Agent

Describe a part made of these primitives and the CAD Agent writes the OpenSCAD for you, with adjustable sliders. The button only fills in the prompt.

Frequently asked questions

Related articles

Tools for thisAll tools

CAD AgentDescribe a part in plain English and get editable OpenSCAD with a live 3D preview and STL or 3MF export.

Watch it doneVideo library

0:57 Parametric CAD from a photo using PrintPalTools 0:25 turn text to mechanical parts for 3D printingTools 2:12 CAD Agent, but the Prompts DoubleIdeas

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