How many sides can it have?

Anything from three to twelve. Three gives a tetrahedron-like point, four the familiar square pyramid, and above about eight it starts to read as a cone with facets.

Is the height the slant or the vertical?

The vertical height, from the middle of the base straight up to the tip. The slant length of each face is worked out from that and the base, so you never have to do the trigonometry.

It prints as a flower: the base polygon in the middle with a triangular face folding up from every edge, and a glue tab on one side of each face. Fold every base edge up, then glue each tab behind the next face, leaving the last one until you have filled it.

How tall are the faces compared to the height I typed?

Taller, because they lean outwards. A seven-sided pyramid with 60 mm sides standing 80 mm tall has faces about 101 mm from base edge to tip, and folded corner edges of about 106 mm. The tool works both out; what matters to you is that they decide whether the net still fits your paper.

At what point should I use a cone instead?

Somewhere around ten sides. Past that the faces are narrow enough that folding them accurately by hand is more trouble than it is worth, and a cone gives you the same silhouette in one piece with a single seam.

Polygonal Pyramid Template — 3 to 12 Sides

The pyramid, opened on seven sides

This is the same generator as the pyramid template, set to a seven-sided base because that is the case people come looking for when they type "polygonal pyramid". Turn the sides down to four and you have an ordinary square pyramid; turn them up and it approaches a cone.

How the net is laid out

One piece: the base polygon in the middle, with a triangular face hinged off every edge and a glue tab on the leading edge of each face. Nothing is cut apart, so there is no lining up of separate pieces — score every base edge, fold the faces up, and glue each tab behind its neighbour.

If you want it hollow

Fill or hang it before you close the last face. Once the final tab is glued the inside is sealed, and a pyramid is one of the harder shapes to open again without tearing a face.

The height you type is not the height you cut

This is the thing people get wrong on a pyramid. The height field is the vertical height — base to tip, straight up, the number you would measure with the pyramid standing on a table. The faces printed on the sheet are taller than that, because each one leans outwards.

On the seven-sided pyramid this page opens with — 60 mm sides, 80 mm tall — each triangular face measures about 101 mm from its base edge up to the tip, and the folded edge running from a base corner to the point is about 106 mm. Both are worked out for you, but they are what decides whether the net fits your paper, so it is worth knowing they are there.

How many sides to choose

Three gives a sharp, tetrahedron-like spike. Dramatic, and it uses the least card of any of them.
Four is the pyramid everyone pictures, and the only one that sits flat against a wall or into a corner.
Five to seven is where it stops looking like a school project and starts looking designed. Seven is deliberately odd: no face sits opposite another, so it reads differently from every angle.
Eight and up reads as a faceted cone rather than a pyramid, and the faces get narrow enough that folding them accurately is fiddly. Past about ten, use the cone instead — one smooth piece, one seam, far quicker.

How much paper it wants

The net is a flower: the base polygon in the middle with every face folded out flat around it, so it spreads roughly twice the slant height across in each direction. The seven-sided example above comes out at about 319 × 311 mm, which is over A4 whichever way you turn the sheet. Either bring the height down — the net narrows quickly as the pyramid gets squatter — or print on A3. A pyramid is a single net, so there is nothing to share out across pages, and it is never split: the tool offers A3 or the largest pyramid that fits your paper.

One consequence of the flower layout worth knowing: the sheet is mostly empty in the corners, because a circle of faces does not fill a rectangle. If you are printing a run, nest a second small template into that dead space rather than feeding a fresh sheet for every pyramid.

Questions

How many sides can it have?: Anything from three to twelve. Three gives a tetrahedron-like point, four the familiar square pyramid, and above about eight it starts to read as a cone with facets.
Is the height the slant or the vertical?: The vertical height, from the middle of the base straight up to the tip. The slant length of each face is worked out from that and the base, so you never have to do the trigonometry.
How is it assembled?: It prints as a flower: the base polygon in the middle with a triangular face folding up from every edge, and a glue tab on one side of each face. Fold every base edge up, then glue each tab behind the next face, leaving the last one until you have filled it.
How tall are the faces compared to the height I typed?: Taller, because they lean outwards. A seven-sided pyramid with 60 mm sides standing 80 mm tall has faces about 101 mm from base edge to tip, and folded corner edges of about 106 mm. The tool works both out; what matters to you is that they decide whether the net still fits your paper.
At what point should I use a cone instead?: Somewhere around ten sides. Past that the faces are narrow enough that folding them accurately by hand is more trouble than it is worth, and a cone gives you the same silhouette in one piece with a single seam.

The pyramid template · Gem stone box · Cone · Polyhedron nets · All box templates

Polygonal pyramid