You can buy a lot of sphere puzzles but often the pieces in the set are arbritarily selected. Therefore I decided to make up some polyspheres from different materials such as marble, glass and wood to get complete sets. Especially table tennis balls are cheap and easy to glue.

Polyspheres in the face-centered cubic lattice are a good possibility to join polyhexes and polyominoes in a common set, because there are planes with hexagonal(blue) and orthogonal (red) grids as shown below.

Besides the tetrahedrons shown above, octahedrons, square pyramids and roofs are favoured solids to build.

The following table shows some sets with different pieces, which can be used to get a lot of constructions.

Set Pieces Size Total Volume Constructions
Planar in the Hexagonal Grid 74 28 acorn
Planar 114 44 size 4 octahedron, 3x8 roof
Non-Planar 14 4 56 size 6 tetrahedron
Planar and Non-Planar 25 4 100 8x5 roof
Planar in the Hexagonal Grid 22 5110 3x19 roof, 4x12 roof
Planar 335 165 size 9 tetrahedron, three square pyramids, three size 6 tetrahedrons with one missing corner
Planar and Non-Planar 210 5 1050 six 6x10 roofs, 21 4x6 roofs, sets of tetrahedrons, sets of square pyramids
Planar in the Hexagonal Grid 82 6496 8x16 roof
Planar 116 6 696 two 8x12 roofs, three square pyramides with one tetrahedron, three hexagons connected by rectangles

More constructions are possible, if you use
sets of equal polyspheres. Such problems were analyzed also by Torsten Sillke some time ago.