Regular Polygon¶

In one sentence: Draw a regular polygon (equilateral triangle through regular octagon, or any N-sided polygon) inscribed in a circle, fully constrained with all sides equal and all interior angles equal.

Overview¶

Workbench: Sketcher · Menu: Sketch → Sketcher geometries → Polygon
Toolbar: Sketcher Geometries (Polygon dropdown) · Shortcut: G, P, 3 (default: Triangle)

The Polygon dropdown contains preset tools for the most common polygons plus a general tool:

Tool	Shortcut	Sides
Triangle	`G, P, 3`	3
Square	`G, P, 4`	4
Pentagon	`G, P, 5`	5
Hexagon	`G, P, 6`	6
Heptagon	`G, P, 7`	7
Octagon	`G, P, 8`	8
Regular Polygon (custom)	—	User-specified N

All variants work the same way: click the centre, click a corner or a midpoint of a side, and FreeCAD draws the polygon inscribed in the circle through that second point.

Intuition¶

Think of drawing a circle, then equally spacing points around it, and connecting adjacent points with straight lines. Regular Polygon automates this: you set the centre and the circumscribed circle radius, and FreeCAD draws all the sides and adds Equal constraints so every side is the same length.

The circle used for construction is drawn as a construction element (dashed) — it exists as a constraint helper but does not form part of the profile that Part Design extrudes. You can constrain its radius to fix the polygon size.

When to use it¶

You need a hex boss, hex socket, or hex flat pattern (Hexagon is the most-used variant for M-thread fasteners).
You need any regular polygon face as a cross-section for a Pad, Pipe, or Loft.
You want a quick equilateral triangle as a construction reference.

When NOT to use it¶

You need an irregular polygon — draw individual lines with angle and distance constraints.
You need a polygon aligned flat-to-flat rather than point-to-point — by default the polygon is inscribed (circumscribed circle goes through corners). For a flat-to-flat width (often needed for hex bolts), apply a Radius/Diameter constraint to the construction midpoint circle and use the inscribed circle radius instead (see Advanced usage).

Step-by-step walkthrough¶

Select the number of sides from the dropdown (e.g. Hexagon = G, P, 6). For a custom count, select Regular Polygon and enter the number when prompted.
Click the centre point of the polygon.
Click a vertex of the polygon (sets the circumscribed radius and the orientation angle). The polygon is drawn immediately.
Constrain the polygon:
- Add a Radius/Diameter constraint to the construction circle to fix the circumscribed radius (= distance from centre to corner).
- Fix the centre position with Lock Position or Coincident.
- Fix the orientation by applying a Horizontal or Angle constraint to one side.

Tip

For a hexagon aligned with flat sides horizontal (wrench-flat orientation), draw the hexagon and then add a Horizontal constraint to one of the flat sides.

Parameters¶

Parameter	Type	Applied via
Number of sides	Integer	Set at creation (dropdown or dialog)
Circumscribed radius	Distance	Radius/Diameter on the construction circle
Centre position	Coordinate	Lock Position or Coincident
Orientation angle	Angle	Angle on one side

Advanced usage¶

Flat-to-flat width (inscribed circle)¶

For hex bolts and similar parts, the key dimension is the flat-to-flat width (the diameter of the inscribed circle, also called the "across-flats" or AF dimension). The tools here size to the circumscribed circle (corner-to-corner).

To constrain the flat-to-flat width:

Draw the hexagon as normal.
Add a Dimension or Distance between the midpoints of two opposite sides. This sets the flat-to-flat distance.
Remove the circumscribed circle radius constraint if you added one (it would be redundant).

Alternatively, use the construction circle to represent the inscribed circle: delete the initial constraint on the construction circle, add a Point at a side midpoint, and constrain that point to be on the construction circle.

Custom N-sided polygon¶

Select Regular Polygon from the dropdown. A dialog asks for the number of sides. Enter any integer ≥ 3. The resulting polygon has N sides with Equal constraints on all sides and internal geometry exactly like the preset tools.

Common mistakes and pitfalls¶

Polygon rotates unexpectedly when dimensions change

Cause: The polygon's orientation angle is not constrained — it has one remaining rotational degree of freedom.
Fix: Add a Horizontal or Vertical constraint to one side, or use Angle to fix the first side's angle.

Circumscribed vs inscribed radius confusion

Cause: The construction circle passes through the corners (circumscribed circle). If you type an M10 hex flat-to-flat dimension as the circumscribed radius, the polygon will be the wrong size.
Fix: For flat-to-flat sizing, constrain the midpoint-of-side distance (the inscribed circle radius) instead. The two are related by r_inscribed = r_circumscribed × cos(π/N).

Python API¶

Minimal example — hexagon¶

import FreeCAD as App
import Sketcher
import Part
import math

doc = App.activeDocument()
sketch = doc.getObject("Sketch")

# Hexagon inscribed in radius R, centre at origin, flat-top orientation
R = 10.0
N = 6
ids = []
pts = [App.Vector(R * math.cos(2 * math.pi * i / N + math.pi / 6),
                   R * math.sin(2 * math.pi * i / N + math.pi / 6), 0)
       for i in range(N)]

for i in range(N):
    ids.append(sketch.addGeometry(
        Part.LineSegment(pts[i], pts[(i+1) % N]), False))

# Join corners
for i in range(N):
    sketch.addConstraint(Sketcher.Constraint(
        "Coincident", ids[i], 2, ids[(i+1) % N], 1))

# All sides equal
for i in range(1, N):
    sketch.addConstraint(Sketcher.Constraint("Equal", ids[0], ids[i]))

# Pin centre (first corner distance from origin = R)
# TODO: verify — add circumscribed radius constraint
doc.recompute()