2004/07/22

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 |
---|---|---|---|---|

Tetraspheres | ||||

Planar in the Hexagonal Grid | 7 | 4 | 28 | acorn |

Planar | 11 | 4 | 44 | size 4 octahedron, 3x8 roof |

Non-Planar | 14 | 4 | 56 | size 6 tetrahedron |

Planar and Non-Planar | 25 | 4 | 100 | 8x5 roof |

Pentaspheres | ||||

Planar in the Hexagonal Grid | 22 | 5 | 110 | 3x19 roof, 4x12 roof |

Planar | 33 | 5 | 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 |

Hexaspheres | ||||

Planar in the Hexagonal Grid | 82 | 6 | 496 | 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

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