Pentomino shapes
A pentomino is five equal squares joined edge to edge. There are exactly 12 shapes, each named after a letter. Here is every piece with its picture, how many ways it can turn and flip, a trick to remember it, and where it fits best.
The 12 pentominoes cover 60 squares, so they can fill a 6×10 rectangle — in 2,339 different ways. This is one of them, with each piece labelled.
flipped version is different · no turn symmetry
A lowercase f leaning on a pole: a 3-tall stem with one square sticking out at the top right and one at the middle left.
Tip: Awkward in corners — it covers one in fewer than 1 in 10 of the 6×10 solutions. Fit it in the middle.
has a mirror line · looks the same after a 180° turn
Five squares in a straight line — the only piece you cannot bend.
Tip: Put it along an edge early: it touches the border in 99.5% of 6×10 solutions.
flipped version is different · no turn symmetry
A line of four with a foot: think of a capital L that grew tall.
Tip: A natural corner piece — it sits in a corner in about half of all 6×10 solutions.
flipped version is different · no turn symmetry
Two bars of 2 and 3 squares that slid past each other, like a slipped L.
Tip: Its mirror image is easy to miss. Flip it before you give up on a gap.
flipped version is different · no turn symmetry
A 2×2 square with a one-square tail: the head and stem of the letter P.
Tip: The most flexible piece (304 positions on a 6×10). Save it for the last awkward gap.
has a mirror line · no turn symmetry
A capital T with a long stem: three across the top, two hanging down.
Tip: Its bar fits flat against a wall; the stem points into the board.
has a mirror line · no turn symmetry
A cup or a horseshoe: three along the bottom and two walls.
Tip: The gap inside the cup can only be filled from outside — often by the X or another piece's nub.
has a mirror line · no turn symmetry
A big corner: two arms of three squares meeting at a right angle.
Tip: The best corner piece — it fills a corner in 54% of 6×10 solutions.
has a mirror line · no turn symmetry
A staircase of three steps.
Tip: Makes jagged edges. Pair it with the Z or N so the steps lock together.
Looks the same after any turn or flip
A plus sign: one square with a neighbour on every side.
Tip: Only 32 positions on a 6×10 and it can never touch a corner — place it first.
flipped version is different · no turn symmetry
A line of four with one bump on the second square.
Tip: Like the P, it can rescue odd leftover spaces. Keep one of the two for the end.
flipped version is different · looks the same after a 180° turn
A Z or S bend: a 3-square middle with one square going each way at the ends.
Tip: Has 2-fold turn symmetry but is not the same when flipped: the S is its mirror.
“Corner” and “edge” = share of the 2,339 computed 6×10 solutions in which the piece covers a corner square or touches the border.
Turning a piece 90° at a time and flipping it over gives up to 8 positions. Symmetric pieces repeat themselves, so they have fewer. Across all 12 pieces there are 63 different positions — that is what a solver has to try.
| Piece | Turns only | Turns + flips | Fits on 6×10 |
|---|---|---|---|
| F | 4 | 8 | 256 ways |
| I | 2 | 2 | 56 ways |
| L | 4 | 8 | 248 ways |
| N | 4 | 8 | 248 ways |
| P | 4 | 8 | 304 ways |
| T | 4 | 4 | 128 ways |
| U | 4 | 4 | 152 ways |
| V | 4 | 4 | 128 ways |
| W | 4 | 4 | 128 ways |
| X | 1 | 1 | 32 ways |
| Y | 4 | 8 | 248 ways |
| Z | 2 | 4 | 128 ways |
| Total | 41 | 63 | — |
Remember the set as “FILiPiNo” (F, I, L, P, N) plus the last seven letters of the alphabet, T U V W X Y Z. Then group them by feel:
Tip from the data: in our 2,339 computed 6×10 solutions, the V or L fills a corner about half the time, while the F (8.5%) and W (14%) rarely do and the X never can.
Print the free pentomino pieces and worksheets, then try the strategy in how to solve a pentomino puzzle. Pick any board in the pentomino solver to see the pieces fit together, browse all 2,339 6×10 solutions, or play the free online polyomino puzzle and packing puzzle.
There are 12 pentominoes if a piece and its mirror image count as the same shape. Counting mirror images separately there are 18, and counting every turned and flipped position there are 63.
Each is named after the letter it looks like: F, I, L, N, P, T, U, V, W, X, Y and Z. A handy way to remember them: “FILiPiNo” plus the last seven letters of the alphabet, T to Z.
Six of them: I, T, U, V, W and X have a mirror line. The other six — F, L, N, P, Y and Z — turn into a different-looking piece when you flip them over.
The X. It fits in only 32 positions on a 6×10 board and can never cover a corner square, so most solvers place it first.
Yes. Some books use John Conway’s letters, which call the I “O”, the L “Q”, the F “R” and the N “S”. PuzzlePave uses the more common F–Z letter names.
A tetromino has 4 squares and there are only 5 shapes; a pentomino has 5 squares and there are 12. Hexominoes, with 6 squares, have 35 shapes.