Catalogue of Polyhops

Polyhop is Kate Jones's name for a plane figure made by joining squares in a hopscotch grid. Thomas Atkinson was the first to describe polyhops. Here I show all the polyhops of orders 1 through 5.

Free polyhops may be reflected as well as rotated. One-sided polyhops may be rotated but not reflected.

Polyhop pieces are available as a game, Hopscotch, from Kadon Enterprises.

In 2000, Livio Zucca defined PolyBricks, which are structurally equivalent to polyhops.

Enumeration

Two-sided polyhops may be reflected or flipped over. One-sided polyhops may not.

Cells Two-Sided
A057973 One-Sided
A197550

1 1 1

2 2 3

3 5 7

4 16 28

5 55 99

6 225 433

7 949 1 852

8 4 269 8 463

9 19 500 38 798

Cells	Two-Sided A057973	One-Sided A197550
1	1	1
2	2	3
3	5	7
4	16	28
5	55	99
6	225	433
7	949	1 852
8	4 269	8 463
9	19 500	38 798

For more values, follow the links in the headings.

Monohop

Dihops

Trihops

Tetrahops

Pentahops

Last revised 2026-01-30.

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Col. George Sicherman [ HOME | MAIL ]