Pentacubes in a Box. Join copies of a pentacube to make a rectangular prism. | |

Pentacubes in a Box Without Corners. Join copies of a pentacube to make a rectangular prism with its corner cells removed. | |

Pentacubes in a Box With Four Edges Removed. Join copies of a pentacube to make a rectangular prism from which the cells along four parallel edges have been removed. | |

Pentacubes in a Box With All Edges Removed. Join copies of a pentacube to make a rectangular prism from which the cells along the edges have been removed. | |

Pentacube Pair Boxes. Join copies of two pentacubes, using one of each, to make a rectangular prism. | |

Pentacube Pair Odd Boxes. Join copies of two pentacubes, using one of each, to make a rectangular prism with odd dimensions. |

Polycube Prisms. Join copies of a polycube to make a prism. | |

Tiling L Shapes with a Pentacube. Join copies of a pentacube to make an L-shaped prism. | |

L Shapes from Pentacube Pairs. Join copies of two pentacubes to make an L-shaped prism. | |

L Shapes from the 29 Pentacubes. Join the 29 pentacubes to make an L-shaped prism. | |

Tiling a Triangular Prism Polycube with a Tetracube. Find a triangular prism polycube that can be tiled with copies of a given tetracube. | |

Tiling a Pyramid Prism Polycube with a Tetracube. Find a pyramid prism polycube that can be tiled with copies of a given tetracube. | |

Tiling a Diamond Prism Polycube with a Tetracube. Find a diamond prism polycube that can be tiled with copies of a given tetracube. | |

Tiling a Triangular Prism Polycube with Two Pentacubes. Find a triangular prism polycube that can be tiled with two given pentacubes, using at least one of each. | |

Tiling a Pyramid Prism Polycube with Two Pentacubes. Find a pyramid prism polycube that can be tiled with two given pentacubes, using at least one of each. | |

Tiling a Diamond Prism Polycube with Two Pentacubes. Find a diamond prism polycube that can be tiled with two given pentacubes, using at least one of each. |

Polycube Reptiles. Join copies of a polycube to make a larger copy of itself. | |

Polycube Bireptiles. Join two copies of a polycube, then dissect the result into equal smaller copies of it. | |

Proper Minimal Polycube Irreptiles. Join variously sized copies of a polycube to make a larger copy of itself, using fewer copies than would be needed if they were all the same size. | |

Prime Boxes for the Clip Pentakedge. Identify the irreducible boxes that can be tiled by the Clip Pentakedge. | |

3^{3} + 4^{3}
+ 5^{3} = 6^{3}.
Dissect a cube of side 6 to make cubes of sides 3, 4, and 5. | |

Tiling a Solid Diamond Polycube With Right Tricubes. Dissect an octahedron-shaped polycube into L-shaped tricubes. | |

Symmetric Pentacube Triples. Join three different pentacubes to form a symmetric polycube. | |

Pentacube Pair Pyramids. Join copies of two pentacubes to make a pyramid. | |

Tiling a Cubic Polycube with Two Pentacubes. Join copies of two pentacubes to make a cube with side 5. | |

Tiling a Rhonic Polycube with Two Pentacubes. Join copies of two pentacubes to make a polycube shaped like a rhombic dodecahedron. | |

Tiling a Cuboctal Polycube with Two Pentacubes. Join copies of two pentacubes to make a polycube shaped like a cuboctahedron. | |

Tiling a Heavy Cuboctal Polycube Shell with Pentacubes. Excise a heavy cuboctal polycube from a bigger one and tile the residue with copies of two or three pentacubes. | |

Filling Space with the Pansymmetric Heptacube. Use the 3D analogue of an X pentomino to fill space. | |

Tiling a Scaled Pentacube with a Pentacube. Use a pentacube to tile various pentacubes scaled up by 2 or 3. | |

Prisms with Square-Symmetric Bases from the 29 Pentacubes. Use all 29 pentacubes to form a prism whose base is a fully-symmetric 29-omino. | |

Twisted Polycube Rings. Construct a re-entrant polycube with a twist in its loop. | |

Entangled Polycubes. Make a rectangular box out of polycubes that cannot be separated. |

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Col. George Sicherman [ HOME | MAIL ]