Upholstery foamFoam is the structural material most soft puppets are built ... More is the dense polyurethane foam sold in craft and fabricFabric is the outer surface of a puppet — the skin, the cl... More shops for cushions, and it is the material most first puppets are mistakenly built from.
Why beginners end up with it
It is the only foam most shops stock, it is cheap, and it is sold in useful-looking blocks. Nothing about the packaging suggests it is the wrong choice for a puppet head.
What goes wrong
It is closed-cell or nearly so, meaning air does not pass through it. A hand and forearm sealed inside that head under stage lights get hot within minutes and stay hot. It is also dense, so a carved skull comes out heavy — and weight is what makes a performer’s arm sag by minute forty, which an audience reads as the character losing interest.
It also fights the glue
Contact cementContact cement is a flexible solvent-based adhesive applied ... works by penetrating the surface and gripping the cell structure. On a closed surface it sits on top instead, and the bond is weaker for it.
Where it is genuinely useful
Body cores, bases, mockups, and any bulk shape you are going to carve away and cover. If a piece does not have a hand inside it and does not carry the silhouette, upholstery foam is fine and cheap.
The alternative
is reticulated foamReticulated foam is open-cell polyurethane foam that has had... — open-cell, breathable, light, and available from specialist suppliers rather than craft shops. Hold a piece to a lamp: if you can see light through it, it is the right stuff.
The hack: build one head from each and hold them. The weight difference settles the argument faster than any explanation.