Pentacube Odd Pairs

A pentacube is a solid made by joining 5 equal cubes face to face.

The blue pentacubes have distinct mirror images. The symbols in green are Kate Jones's names for the pentacubes.

A compatibility figure for two or more polyforms is a figure that can be tiled with any of them. In 2004, Livio Zucca published Pentomino Odd Pairs, showing minimal known compatibility figures for every pair of pentominoes, using an odd number of each.

Here I show minimal known compatibility figures for every pair of pentacubes, using an odd number of each. A prime mark (′) after a letter denotes a mirror image. For example, S′ is the mirror image of S. To see a tiling, click on the corresponding entry in the table below. Missing entries indicate unsolved cases. If you solve an unsolved case, or find a smaller solution than one given here, please write.

See also Pentacube Compatibility.

A 33933213337553539599737
B  333353533333353535535
E   333333153335533333555535935
F    3353535333355555735
G      3351533335353333579372555
H        393333733333535353935
I       315355713115555555
J           333533333553335933
K         579333333751533
L          93335333352333
M           733397997357
N            333355331537
P             3333333733
Q              3373331735
R                   3335573933
S                     3337533
T                 3791739
U                  79511
V                   957
W                    1955
X                     515
Y                      5

Last revised 2022-02-24.

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Col. George Sicherman [ HOME | MAIL ]