Tiling a Polyomino at Scale 2 with a Tetromino
and a Pentomino
A tetromino is a figure made of 4 squares joined
edge to edge.
There are 5 such figures, not distinguishing reflections and rotations.
A pentomino is a figure made of 5 squares joined
edge to edge.
There are 12 such figures, not distinguishing reflections and rotations.
Here I study the problem of arranging copies
of a tetromino and a pentomino
to form some polyomino that has been scaled up by a factor of 2.
See also
This table shows the areas of the smallest polyominoes
that can be tiled by a tetromino and a pentomino,
using at least one copy of each.
The green indexes are links to tilings by the specified tetromino alone.
The blue indexes are links to tilings by the specified pentomino alone.
| F | I | L | N | P | T | U | V | W | X | Y | Z |
I | 36 | 24 | 24 | 40 | 24 | 36 | 72 | 28 | 72 | ? | 24 | 28 |
L | 28 | 24 | 24 | 28 | 24 | 36 | 36 | 28 | 36 | 36 | 28 | 28 |
N | ? | 44 | 32 | ? | 24 | 36 | 36 | 68 | ? | ? | 32 | 48 |
Q | ? | 24 | 24 | 96 | 24 | 64 | ? | 24 | ? | ? | 28 | 24 |
T | 36 | 32 | 24 | 36 | 24 | 36 | 36 | 36 | 36 | 68 | 28 | 36 |
So far as I know, these solutions
use as few tiles as possible. They are not necessarily uniquely minimal.
24 Cells
28 Cells
32 Cells
36 Cells
40 Cells
44 Cells
48 Cells
64 Cells
68 Cells
72 Cells
96 Cells
Last revised 2025-05-07.
Back to Polyomino and Polyking Tiling
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Polyform Curiosities
Col. George Sicherman
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