other numbers of nets

tetrahedron

it is fairly easy to prove that there are only two different nets for a tetrahedron,
e.g. by considering where edges can be broken
maybe using Polydron

octahedron
the octahedron has 11 different nets, the same as the cube:

square based pyramid
a square based pyramid has 6 different nets:

regular triangular dipyramid (bipyramid)

this shape is two tetrahedrons, fitted together face-to-face:

Tandi Clausen-May identifies 8 different nets for the triangular dipyramid

of the 12 hexiamonds, all of the top row, all of the third row and all of the left column form nets of this solid














thanks to Puntmat