Tetrahex Oddities

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These puzzles use multiple sets of tetrahexes. The challenge is to create a symmetric pattern using an odd number of copies of the chosen piece or pieces. The results shown are the best known solutions - please let me know if you can do better.

 

Oddities using copies of only one piece were first studied by Torsten Sillke and are also known as Sillke Figures. Results for Tetrahex Oddities of this type can be found here at George Sicherman's site. George allows a single pattern to count for any lower symmetries that it satisfies, whereas I do not. He also sent many improved results, which are marked with an asterisk.

 

One-Piece Oddities - see solutions

Piece

Vertical Horizontal Birotary Double Bilateral Sextarotary Full Ternary & Horizontal Ternary & Vertical Trirotary

1

3

3

3

1

15

9

9*

3

3

2

3

3

3*

5*

9

3

3

3

3

3

3*

3*

1

3

X

X

3

9*

3

4

X

3

X

X

X

X

1

?

3

5

1

5

5

3

9

3

3

3

3

6

3

3

3

5

9

3

7*

3

3

7

3

3

3

1

X

X

9*

3

3

 

Two-Piece Oddities - see solutions

Pieces

Vertical Horizontal Birotary Double Bilateral Sextarotary Full Ternary & Horizontal Ternary & Vertical Trirotary

12

3

3

3

5

9

9

7*

7

7

13

3

3

3

3

15

15

9

7

7*

14

3

3

3

3

15

15

7

9

7

15

3

3

3

3

9

9

9

9

7*

16

3

3

3

3

9

9

9

7

7

17

3

3

3

3

15

9

9

9

9

23

3

3

3

3

9

9

7

7*

7

24

3

3

5

5

9

9

7

7

7

25

3

3

3

5

9

9

9

7

7

26

3

3

3

5

9

9

7*

7

7

27

3

3

3

5

9

9

9

3

7

34

5

3

3

5

?

?

7

9*

7

35

3

3

3

3

9

9

7*

9

9

36

3

3

3

3

9

9

7*

7

7

37

3

3

3

3

?

?

7

7

7

45

3

3

5

5

9

9

7

9

7

46

3

3

5

5

9

9

7

7

7

47

3

3

3

3

?

?

7

9

7

56

3

3

3

3

9

9

7

7

7

57

3

3

3

3

9

9

7

9

7*

67

3

3

3

5

9

9

7*

7

7

Three-Piece Oddities -  see solutions

Pieces

Vertical Horizontal Birotary Double Bilateral Sextarotary Full Ternary & Horizontal Ternary & Vertical Trirotary
123 5 3 5 5 9 9 7* 7 7
124 3 3 5 5 9* 9 7 7 7
125 3 3 3 3 9 9 7 7 7
126 3 3 3 3 9 9 7 7 7
127 3 3 5 5 9 9 7* 7 7
134 5 3 5 5 15 9* 7 7 7
135 3 3 5 5 9* 15 9 9 7*
136 3 3 5 5 9 9 7* 7 7
137 3 3 3 5 9 15 7 7 7
145 3 5 5 5 15 15 7 9 7
146 5 3 5 5 9* 9 7* 7 7
147 5 3 5 5 15 15 7 7 7
156 3 3 3 5 9 9 7* 7 7
157 3 3 5 5 9 9 7 9 7
167 3 3 5 5 9 9 7* 7 7
234 5 3 5 5 9* 9 7 7 7
235 3 3 3 3 9 9 7 7* 7
236 3 3 3 3 9 9 7* 7 7
237 3 3 5 5 9* 9 7* 7* 7
245 3 3 5 5 9 9 7 7* 7
246 3 3 3 3 9 9 7 7 7
247 5 3 5 5 15 9 7 9 7
256 3 3 3 3 9 9 7 3 7
257 3 3 3 3 9 9 7* 3 7
267 3 3 3 3 9 9 7* 3 7
345 5 3 5 5 9* 15 7 9 7
346 3 3 5 5 9 9 7 7 7
347 3 3 3 3 ? ? 7 7* 7
356 3 3 3 5 9 9 7 7* 7
357 5 5 5 5 15 9 7 7* 7
367 3 3 5 5 9 9 7 7 7
456 3 3 3 3 9 9 7 7 7
457 5 5 5 5 15 9 7 7* 7
467 3 3 5 5 9 9 7 7 7
567 3 3 3 3 9 9 7 3 7

 

Four-Piece Oddities - see solutions

Pieces

Vertical Horizontal Birotary Double Bilateral Sextarotary Full Ternary & Horizontal Ternary & Vertical Trirotary
1234 5 5 5* 7 9 9 7 7 7
1235 5 5 5 5 9* 9 7 7 7
1236 5 5 5 5 9 9 7 7 7
1237 5 5 5 7 9 9 7 7 7
1245 5 5 5 5 9* 9 7* 7* 7
1246 5 5 5 5 9 9 7 7 7
1247 5 5 5* 7 15 9 7 9 7
1256 5 5 5 5 9 9 7 7 7
1257 5 5 5 5 9 9 7 7 7
1267 5 5 5 5 9 9 7* 7 7
1345 5 5 5* 7 15 9 7 7 7*
1346 5 5 5 5 9 9 7 7 7
1347 5 5 5 5 15 15 9 7 7
1356 5 5 5 5 9 9 7 7 7
1357 5 5 5* 5* 15 9 7 7 7
1367 5 5 5 5 9 9 7 7 7
1456 5 5 5 5 9* 9 7 7 7
1457 5 5 5* 7 9* 9 9* 9 7*
1467 5 5 5 5 15 9 7 7 7
1567 5 5 5 5 9 9 7 7 7
2345 5 5 5 5 9 9 7 7 7
2346 5 5 5 5 9 9 7 7 7
2347 5 5 5 5 15 9 7 7 7
2356 5 5 5 5 9 9 7 7 7
2357 5 5 5 5 9 9 7 7* 7
2367 5 5 5 5 9 9 7 7 7
2456 5 5 5 5 9 9 7 7 7
2457 5 5 5 5 15 9 7 9 7
2467 5 5 5 5 9 9 7 7 7
2567 5 5 5 5 9 9 7 7 7
3456 5 5 5 5 9 9 7 7 7
3457 5 5 5 5 15 9 7 7 7
3467 5 5 5 5 9 9 7 7 7
3567 5 5 5 5 9 9 7 7 7
4567 5 5 5 5 9* 9 7 7 7

 

Five-Piece Oddities - see solutions

Pieces

Vertical Horizontal Birotary Double Bilateral Sextarotary Full Ternary & Horizontal Ternary & Vertical Trirotary
12345 5 5 5* 7 9 9 7 7 7
12346 5 5 5 5 9 9 7 7 7
12347 5 5 7 7 15 9 7 7 7
12356 5 5 5 5 9 9 7 7 7
12357 5 5 5 5 9 9 7 7 7
12367 5 5 5 5 9 9 7 7 7
12456 5 5 5 5* 9 9 7 7 7
12457 5 5 5 7 9 9 7 9 7
12467 5 5 5 7 9 9 7 7 7
12567 5 5 5 5 9 9 7 7 7
13456 5 5 5 5 9 9 7* 7 7
13457 5 5 7 7 9 9 9 7 7
13467 5 5 7 7 9 9 7 7 7
13567 5 5 5 5 9 9 7 7 7
14567 5 5 5 5 9 9 7 7 7
23456 5 5 5 5 9 9 7 7 7
23457 5 5 5* 5 15 9 7 7 7
23467 5 5 5 5 9 9 7 7* 7
23567 5 5 5 5 9 9 7 7 7
24567 5 5 5 5 9 9 7 7 7
34567 5 5 5 5 9 9 7 7 7

 

Six-Piece Oddities - see solutions

Pieces

Vertical Horizontal Birotary Double Bilateral Sextarotary Full Ternary & Horizontal Ternary & Vertical Trirotary
123456 7 7 7 7 9 9 7 7 7
123457 7 7 7 7 9 9 7 7 7
123467 7 7 7 7 9 9 7 7 7
123567 7 7 7 7 9 9 7 7 7
124567 7 7 7 7 9 9 7 7 7
134567 7 7 7 7 9 9 7 7 7
234567 7 7 7 7 9 9 7 7 7

 

Seven-Piece Oddities - see solutions

Pieces

Vertical Horizontal Birotary Double Bilateral Sextarotary Full Ternary & Horizontal Ternary & Vertical Trirotary
1234567 7 7 7 7 9 9 7 7 7

 

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