Additive Prism¶

In one sentence: Add a solid regular-polygon prism — a hexagonal column, triangular pillar, or any n-sided post — directly into a Part Design Body, fusing it with any existing material.

Overview¶

Workbench: Part Design · Menu: Part Design → Additive Primitives → Additive Prism
Toolbar: Part Design Modeling Primitives · Shortcut: none

Additive Prism inserts a parametric prism with a regular polygonal cross-section into the active Body and fuses it with the existing shape. You specify the number of polygon sides, the circumscribed radius (centre to vertex), and the height. Two optional taper angles (FirstAngle and SecondAngle) let you draft the sides to make the prism into a frustum or a tapered post. Because the polygon is always regular and centred at the origin, this is the fastest way to add hex bosses, triangular standoffs, octagonal pillars, and similar repeating features without constructing a sketch.

Intuition¶

A prism is simply any flat polygon pushed straight up to form a solid column. A triangular prism is what a Toblerone box looks like; a hexagonal prism is the shape of a hex bolt head. The cross-section is always a regular polygon — all sides and interior angles are equal.

The Polygon parameter sets how many sides the polygon has. Circumradius is the distance from the polygon's centre to any of its corners (vertices), not to the middle of a flat face. For a hex wrench size of 10 mm across-flats, the circumradius is slightly larger than 5 mm; the exact relationship is:

circumradius = (across-flats / 2) / cos(π / n)

where n is the number of sides. For a hexagon: circumradius = AF / (2 × cos 30°).

The FirstAngle and SecondAngle properties come from the PrismExtension mixin. They tilt the direction of extrusion away from vertical, effectively producing a tapered prism. Both default to 0° (straight vertical extrusion).

When to use it¶

You need a hex boss, square peg, triangular standoff, or any regular-polygon column and don't want to draw and constrain a polygonal sketch.
You are modelling a bolt head, nut profile, or socket drive feature that must be exactly a regular polygon.
You need a tapered prism (a draft angle on all faces) — set FirstAngle or SecondAngle to tilt the extrusion.
You want to quickly prototype a multi-sided post and vary the number of sides parametrically.

When NOT to use it¶

The cross-section is not a regular polygon (e.g. irregular hexagon, rounded corners) — draw the profile in a sketch and use Pad instead.
You need different heights on different sides — the prism always extrudes to a flat top face; use a sketch-based feature for tapered or stepped profiles.
You want to cut a prism-shaped hole or socket — use Subtractive Prism, which has identical parameters but removes material.
The polygon has fewer than 3 sides — FreeCAD enforces a minimum of 3 sides and will report an error if Polygon < 3.

Step-by-step walkthrough¶

Prerequisites: An active Part Design Body in the document. The prism can be the very first feature (no existing solid required).

Open or create a document and ensure a Body is active. FreeCAD will offer to create one automatically if none exists.
Activate Part Design → Additive Primitives → Additive Prism from the menu, or click its icon in the Part Design Modeling Primitives toolbar (expand the drop-down if multiple primitives share one button).
The task panel opens. Set Polygon to the number of sides — 6 for a hex, 3 for a triangle, 8 for an octagon.
Set Circumradius to the distance from the polygon's centre to a vertex.
Set Height to the desired extrusion length.
Leave FirstAngle and SecondAngle at 0° for a straight prism. Set them to non-zero values if you need tapered sides (draft angle).
Click OK. The prism is fused into the Body and appears in the model tree as Prism.

Tip

To match an ISO hex bolt head, measure the "across-flats" (wrench size) and convert to circumradius using circumradius = AF / (2 × cos(30°)) ≈ AF × 0.5774. For example, an M10 hex head with 17 mm across-flats has a circumradius of approximately 9.815 mm.

Parameters¶

Parameter	Type	Default	Description
Polygon	Integer	6	Number of sides of the regular polygon cross-section. Minimum 3.
Circumradius	Length (mm)	2.0	Distance from the polygon centre to a vertex (not to a face midpoint). Must be > 0.
Height	Length (mm)	10.0	Height of the prism (extrusion length along the local Z-axis). Must be > 0.
FirstAngle	Angle (°)	0.0	Taper angle in the first direction. Range: −89.99° to +89.99°. Tilts the extrusion direction away from vertical, creating a draft on the lateral faces.
SecondAngle	Angle (°)	0.0	Taper angle in the second direction, orthogonal to FirstAngle. Range: −89.99° to +89.99°.

Advanced usage¶

Across-flats vs. circumradius¶

The UI uses circumradius (centre to vertex), but engineering drawings typically specify "across-flats" (AF, the distance between two parallel faces). The conversion is:

circumradius = AF / (2 × cos(π / n))

For common polygon counts:

Sides	Factor (circumradius = AF × factor)
3 (triangle)	1 / (2 × cos 60°) = 1.0000
4 (square)	1 / (2 × cos 45°) ≈ 0.7071 (use half-diagonal = AF/2 × √2/2)
6 (hexagon)	1 / (2 × cos 30°) ≈ 0.5774
8 (octagon)	1 / (2 × cos 22.5°) ≈ 0.5412

Note

For a square (4 sides) the circumradius equals half the diagonal length, not half the side length.

Tapered prism (draft angles)¶

Setting FirstAngle to a positive value leans the extrusion in the positive X direction as it grows in Z, while SecondAngle leans it in the Y direction. Both operate on the same extrusion by composing the two tilt components. This is equivalent to a shear-extruded prism and produces laterally tapered faces rather than the constant vertical faces of the default prism.

Typical use case: a tapered knurled grip or a moulded polygonal boss that needs a draft angle for de-moulding.

Combining prism with Pocket for hex socket¶

A common workflow for a hex socket (inward hex hole):

Place an Additive Box or Additive Cylinder as the outer body.
Use Subtractive Prism (with Polygon = 6) to cut the socket. Set Circumradius to the correct hex size and Height to the socket depth.

Common mistakes and pitfalls¶

Polygon value is less than 3

Cause: A polygon with fewer than 3 sides is geometrically impossible. FreeCAD will produce an error: "Polygon of prism is invalid, must have 3 or more sides".
Fix: Set Polygon to 3 or higher.

Circumradius value appears correct but the polygon is smaller than expected

Cause: Circumradius is the centre-to-vertex distance, not the centre-to-face (inradius) distance. If you entered an across-flats value directly as the circumradius, the prism will be smaller than expected.
Fix: Convert using the formula above, or verify by measuring across the flat faces of the generated solid in the viewport.

Prism base is not flat after setting FirstAngle or SecondAngle

Cause: When taper angles are non-zero, the lateral faces are no longer vertical and the apparent width changes along the height.
Fix: This is the intended behaviour. If you need a strictly constant cross- section, reset FirstAngle and SecondAngle to 0°.

Prism is not joined to the existing Body solid

Cause: The prism does not overlap the current Body tip, so no fusion is performed and the result is topologically disconnected.
Fix: Move the Body origin or use the Attachment tool to position the prism so it at least shares a face or intersects the existing solid.

Python API¶

Minimal example¶

import FreeCAD as App
import PartDesign

doc = App.newDocument()

body = doc.addObject("PartDesign::Body", "Body")

prism = doc.addObject("PartDesign::AdditivePrism", "Prism")
body.addObject(prism)

# Default hexagonal prism: 6 sides, circumradius=2, height=10
doc.recompute()

print(f"Volume: {prism.Shape.Volume:.4f} mm³")
# Regular hex with circumradius r, height h: V = (3√3/2) * (r*cos(30°))² * h
# TODO: verify computed volume matches analytic formula

Customising polygon and dimensions¶

prism.Polygon      = 3      # triangle
prism.Circumradius = 8.0    # mm, centre to vertex
prism.Height       = 15.0   # mm
prism.FirstAngle   = 5.0    # 5° draft in X direction
prism.SecondAngle  = 0.0    # no draft in Y direction
doc.recompute()

Resulting feature properties¶

Property	Type	Description
`Polygon`	`App::PropertyIntegerConstraint`	Number of polygon sides. Minimum 3.
`Circumradius`	`App::PropertyLength`	Radius from polygon centre to vertex, mm.
`Height`	`App::PropertyLength`	Prism height along local Z-axis, mm.
`FirstAngle`	`App::PropertyAngle`	Extrusion taper angle in first direction, degrees. Range −89.99° to +89.99°. (from `PrismExtension`)
`SecondAngle`	`App::PropertyAngle`	Extrusion taper angle in second direction, degrees. Range −89.99° to +89.99°. (from `PrismExtension`)