FabLayout

Polygon pyramid flat pattern calculator

A hexagonal, octagonal or other regular polygon hopper or pyramid. Enter the number of sides, the bottom and top edge and the height; you get a fan pattern with both radii.

Get TrueflatRead the steps

Enter your measurements

Your dimensions are measured to the

Export from the Trueflat app

1:1 PDF and DXF files of this flat pattern are made in Trueflat, ready for print, plasma, laser or waterjet. It works offline on site.

App StoreGoogle Play
878.5 mm540.2 mm
Flat pattern: cut on the bold outline, bend on the dashed blue lines, the thin lines are marking lines

Seam

538.5mm

Exact geometry

Edge length
In the app
Cut length
In the app
Sheet size
In the app

Every result is in Trueflat

The free web version shows the main result and the drawing. Trueflat gives you every mark and measurement, and exports a cut sheet. It is free to download.

App StoreGoogle Play

How to lay it out

  1. Swing both arcs

    From a centre point, swing the outer arc at the outer pattern radius and the inner arc at the inner pattern radius.

  2. Step off the bottom edges

    Starting from a radius line, step the bottom edge length along the outer arc as a chord, once for every side.

  3. Draw the corner lines

    Join every mark to the centre. The lines between the arcs are the corners of the pyramid.

  4. Join the chords

    Draw straight chords between neighbouring marks on both arcs; on the inner arc they come out at the top edge length.

  5. Mark bends and seam

    Mark the inner corner lines as bends, use the first and last as seam lines and add your allowance.

Good to know

  • FabLayout runs the same code as Trueflat; the result is exact geometry.
  • Source: Kittredge, The New Metal Worker Pattern Book (1917), Problem 114 "Envelope of a Hexagonal Pyramid", Figs. 430–432, and Problem 115, p. 242

Method and formula

Every face of a regular polygon pyramid is the same isosceles trapezoid, so the faces form a fan around the apex and the pattern is exact.

  • Corner edge e = √(H² + (R1 − R2)²), where R1 and R2 are the corner radii of the bottom and top polygons, R = a ÷ (2 sin(180° ÷ N)).
  • Outer pattern radius L1 = e × a1 ÷ (a1 − a2); inner L2 = L1 − e.
  • Angle per face 2 asin(a1 ÷ (2 L1)); N faces always total less than 360°.

For a pointed pyramid set the top edge to 0; then the inner radius is 0 and the fan runs to the apex. With thickness, a cut-off pyramid can be measured inside, middle or outside: the edge lengths shift, the corner length stays the same. A pointed one is taken to the middle of the sheet only.

Worked example

Hexagon, bottom edge 40 mm, top edge 20 mm, height 30 mm: R1 − R2 = 20 mm, so e = √(900 + 400) = 36.06 mm. L1 = 72.11 mm, L2 = 36.06 mm. Each face takes 32.20°, 193.23° for all six.

Questions

How is this different from the rectangular pyramid?

All the faces here are identical, so the pattern is a single fan around one centre. A rectangular pyramid has two face shapes and is laid out face by face. With 4 sides and a square base, both pages give the same pattern.

Do I enter the edge length or the diameter?

The edge length: the length of one side of the bottom polygon, and of the top polygon if the pyramid is cut off. The calculator works out the corner radii from the number of sides.

How many sides can it have?

From 3 to 16. Six and eight are the usual hopper shapes. For many sides the result approaches a truncated cone.

Similar calculators

More in TrueflatEccentric reducerAngled eccentric reducerOblique coneSee what the app does