A polyform oddity is a shape with even symmetry formed by joining an odd number of copies of a polyform.
Polycubes can belong to any of 33 symmetry classes, including asymmetry; see Polycube Symmetries. Of these symmetry classes, 31 have even order and can be symmetries of oddities.
Here I show minimal oddities for the P pentacube that belong to every even symmetry class. If you find a smaller example for any symmetry class, please write.
For other pentacubes, see Pentacube Oddities with Full Symmetry and its links to other pentacube oddity pages.
C4(2) 3 | B6(2) 5 | CF6(2) 5 | F5(2) 3 |
---|---|---|---|
E4(2) 1* | A12(4) 5* | J10(4) 7 | BC10(4) 7 |
BB10(4) 9 | CK6(4) 5* | BE4(4) 5* | CE3(4) 3 |
BF6(4) 5 | EE4(4) 3 | CD10(6) 5* | FF4(6) 5* |
H12(6) 5* | AB16(8) 9 | EF6(8) 5* | BFF8(8) 7 |
CJ6(8) 9 | AE8(8) 9 | EFF7(8) 7 | EEE6(8) |
BD34(12) 17 | DF6(12) 5* | BBC2(16) 9* | R56(24) 25* |
CCC20(24) 17* | DEE25(24) 25* | G1(48) 25* | |
Last revised 2024-05-12.