Regular Pyramid Frustum flat pattern

What it is

The frustum of a regular s-sided pyramid: two coaxial regular polygons and s identical flat facets. It is the part behind polygonal chimney caps, polygonal hoppers, hexagonal duct and cyclone baskets.

Where it is used

Polygonal chimneys and caps, silo hoppers, hexagonal and octagonal duct, cyclone baskets, oven hoods, any reduction between two regular polygonal mouths.

Measurements the calculation needs

• D1 Diameter 1
• D2 Diameter 2
• H Height
• S Sections
• THK Thickness

Worked example

The values the form comes pre-filled with, run through the tool itself:

Diameter 1	600 mm
Diameter 2	1000 mm
Height	700 mm
Sections	6
Thickness	3 mm
The flat pattern fits a plate of	2060 × 1737 mm

Frequently asked questions

Are the diameters across corners or across flats?

Across corners — the CIRCUMSCRIBED circle, through the vertices. It is the same measure as the cone in this catalogue, deliberately: swap a cone for a polygonal one and you type the same two numbers. Across flats, which is what a caliper gives on a finished hexagon, is d times the cosine of 180/s: on a 600 circumscribed hexagon that is 519.6.

Why does this part not ask for divisions?

Because there is nothing to approximate. Each face has its bottom edge parallel to its top edge, so the face is a flat trapezoid and its development is itself, exactly. The absence of a division count is the proof of it.

Can I make a straight prism, with no reduction?

You can — enter the same diameter twice. The part is then straight polygonal duct, hexagonal or octagonal, and that is a real part rather than a degenerate case.

What if I want four sides?

It works, and gives exactly the same pattern as the Rectangular Transition in the square case — the spec checks it edge by edge. For a rectangular reduction with different proportions at the two mouths, use that part, which takes all four figures separately.

Does thickness come off as it does on a cylinder?

It does not. The mean surface lies half a thickness inside each FACE, which shrinks the apothem by half the thickness and the circumscribed radius by rather more. On a triangle the difference is large, and that is why this part's thickness guard is on the apothem.