Questions 6-10
6: Do the individual pentominoes have names?
Yes, but people confusingly have different names for them.
Golomb came up with these names come from looking at the pieces and calling them by the letter that they look like:
TODO: picture
F I L N P T U V W X Y Z
These names, by John Horton Conway, looks at the pieces and makes them into a sequence of letters from O-Z which is easier to remember:
TODO: picture
O P Q R S T U V W X Y Z
7: If I cut a pentomino out of cardboard, will it fold into a box?
Most of them will
Piece
Fold into a box?
O
No
P
No
Q
Yes
R
Yes
S
Yes
T
Yes
U
No
V
No
W
Yes
X
Yes
Y
Yes
Z
Yes
TODO: cut these out of cardboard and prove it with a photo
8: How many rotations do each of the pentominoes have?
When putting a pentomino on a grid, some pentominoes look the same if you flip them over or rotate them by some amount.
For instance, the X pentomino looks the same if you rotate it 90, 180, or 270 degrees, or if you flip it over, so that's 1 rotation.
The O pentomino (the long skinny straight one) can be rotated 90 degrees, but at 180 degrees, you're back where you started. And flipping it over doesn't change it, so that's 1 for the starting orientation plus 1 for the 90 degree rotation, for a total of 2.
Pentomino
planar rotations
can flip?
total rotations
O
0, 90
No
2
P
0, 90, 180, 270
Yes
8
Q
0, 90, 180, 270
Yes
8
R
0, 90, 180, 270
Yes
8
S
0, 90, 180, 270
Yes
8
T
0, 90, 180, 270
No
4
U
0, 90, 180, 270
No
4
V
0, 90, 180, 270
No
4
W
0, 90, 180, 270
No
4
X
0
No
1
Y
0, 90, 180, 270
Yes
8
Z
0, 90
Yes
4
9 Can you make pentominoes out of hexagons?
Sure, why not? Here's a picture of pentominoes made out of 5 hexagons each. We'll be sticking with square tiles for the rest of this book, though.
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