# Polycube Prisms

An old problem in combinatorial geometry is to find the smallest
solid box that a polycube can tile.
See, for example, Pentacubes in a Box.
Here I show minimal results for a broader problem:
find the smallest prism that a polycube can tile.
Some polycubes that cannot tile boxes can tile prisms.

I do not show flat polycubes, which are prisms in their own right.

[ Tetracubes
| Pentacubes
| Hexacubes
]

### 1 Tile

### 2 Tiles

### 3 Tiles

### 4 Tiles

### 6 Tiles

### 8 Tiles

### Impossible

### Allowing Reflection

Sometimes we can use fewer tiles by letting the hexacube be reflected:

Last revised 2017-10-22.

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Polyform Curiosities

Col. George Sicherman
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