Puzzle piece shapes

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Division of the piece shapes of normal puzzles

A normal puzzle with grid or strip cut consists of pieces with 4 sides and bulges or notches and more or less straight edges, including the edge pieces.

Theoretically possible shapes

For the consistent division of the edge of the pieces, the following classification will be used:

0: the side of the piece has an notch (hole)

1: the side of the piece has a bulge (nose)

2: the side of the pice is neither 0 nor 1 (straight edge or similar)

According to this classification, there can be a total of 3⁴ = 81 different pieces. The usual puzzles nowadays have about 5 to 15 different part shapes (not including rotations).

Glossary

To define a unique notation, the following rule is used:

- Each side of a puzzle piece is given the number 0, 1 or 2 according to the notation above.

- Starting at 12 clockwise, each side of the piece gets this number and thus each puzzle piece gets a 4-digit number.

Example: The puzzle piece 2101 looks like this:

Glossary of puzzle pieces

Piece No.	Digits	Edge top	Edge right	Edge bottom	Edge left	Examples
1	0000	0	0	0	0
2	0001	0	0	0	1
3	0002	0	0	0	2
4	0010	0	0	1	0
5	0011	0	0	1	1
6	0012	0	0	1	2
7	0020	0	0	2	0
8	0021	0	0	2	1
9	0022	0	0	2	2
10	0100	0	1	0	0
11	0101	0	1	0	1
12	0102	0	1	0	2
13	0110	0	1	1	0
14	0111	0	1	1	1
15	0112	0	1	1	2
16	0120	0	1	2	0
17	0121	0	1	2	1
18	0122	0	1	2	2
19	0200	0	2	0	0
20	0201	0	2	0	1
21	0202	0	2	0	2
22	0210	0	2	1	0
23	0211	0	2	1	1
24	0212	0	2	1	2
25	0220	0	2	2	0
26	0221	0	2	2	1
27	0222	0	2	2	2
28	1000	1	0	0	0
29	1001	1	0	0	1
30	1002	1	0	0	2
31	1010	1	0	1	0
32	1011	1	0	1	1
33	1012	1	0	1	2
34	1020	1	0	2	0
35	1021	1	0	2	1
36	1022	1	0	2	2
37	1100	1	1	0	0
38	1101	1	1	0	1
39	1102	1	1	0	2
40	1110	1	1	1	0
41	1111	1	1	1	1
42	1112	1	1	1	2
43	1120	1	1	2	0
44	1121	1	1	2	1
45	1122	1	1	2	2
46	1200	1	2	0	0
47	1201	1	2	0	1
48	1202	1	2	0	2
49	1210	1	2	1	0
50	1211	1	2	1	1
51	1212	1	2	1	2
52	1220	1	2	2	0
53	1221	1	2	2	1
54	1222	1	2	2	2
55	2000	2	0	0	0
56	2001	2	0	0	1
57	2002	2	0	0	2
58	2010	2	0	1	0
59	2011	2	0	1	1
60	2012	2	0	1	2
61	2020	2	0	2	0
62	2021	2	0	2	1
63	2022	2	0	2	2
64	2100	2	1	0	0
65	2101	2	1	0	1
66	2102	2	1	0	2
67	2110	2	1	1	0
68	2111	2	1	1	1
69	2112	2	1	1	2
70	2120	2	1	2	0
71	2121	2	1	2	1
72	2122	2	1	2	2
73	2200	2	2	0	0
74	2201	2	2	0	1
75	2202	2	2	0	2
76	2210	2	2	1	0
77	2211	2	2	1	1
78	2212	2	2	1	2
79	2220	2	2	2	0
80	2221	2	2	2	1
81	2222	2	2	2	2

Note:

1) The piece No. 81 (2222) should not exist, since there is no interlocking connection to the neighboring pieces on any side.

Older puzzles have much more different pieces only by the possibilitiy of the piece side "2". The puzzle 4000 Ramsau, Deutschland of 1974 has even edge pieces with the three other piece sides "2", so that also the piece No. 81 exists.

2) Since the alignment of a piece is clearly fixed first in the finished puzzle, many pieces are equivalent by rotation.

Beispiel: Piece No. 14 (0111) is equivalent to piece No. 40 (1110), No. 38 (1101) and No. 32 (1011). This is shown in the next table.

Equivalent piece shapes

Puzzle pieces with rotation

Piece No.	equivalent No.	Examples
G1	1
G2	2, 4, 10, 28
G3	3, 7, 19, 55
G4	5, 13, 37, 29
G5	6, 16, 46, 56
G6	8, 22, 64, 30
G7	9, 25, 73, 57
G8	11, 31
G9	12, 34, 20, 58
G10	14, 40, 38, 32
G11	15, 43, 47, 59
G12	17, 49, 65, 33
G13	18, 52, 74, 60
G14	21, 61
G15	23, 67, 39, 35
G16	24, 70, 48, 62
G17	26, 76, 66, 36
G18	27, 79, 75, 63
G19	41
G20	42, 44, 50, 68
G21	45, 53, 77, 69
G22	51, 71
G23	54, 80, 78, 72
G24	81