Pentacube Pair Oddities

A pentacube is a solid made of 5 equal cubes joined face to face.

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

A polyform oddity or Sillke Figure is a polyform with binary symmetry at least, tiled by an odd number of copies of a given polyform.

Here I show polycubes with full symmetry formed by joining an odd total number of two different pentacubes. 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.

  ABEE′FGG′HH′IJJ′KLMNPQRR′SS′TUVWXYZ
A  15 21 21 21 21 21 21 21 21 21 21 21 21 15 21 25 21 21 21 27 25 21
B   21 25 33 19 21 21 23 21 23 21 21 21 21 23 23 15 21 21 17 23 23
E    21 25 19 25 23 23 25 21 21 15 21 11 21 21 21 21 21 25 25 25 15 21 21 25 21 25
F     25 33 25 21 25 25 25 25 25 25 25 25 25 15 25 25 23 25 25
G       37 33 33 55 25 25 25 25 27 21 21 21 33 15 33 33 51 25 25 145– 25 55
H         33 25 15 25 25 25 25 25 25 33 29 29 25 25 25 15 21 25 31 25 25
I        25 25 25 5 25 3 25 25 25 25 25 25 25 25 25 25
J            21 15 21 11 21 21 21 25 25 15 25 25 15 21 25 25 21 25
K          21 25 21 21 21 25 51 25 25 25 25 25 25 25
L           21 25 25 21 25 25 25 21 25 25 25 21 25
M            17 17 25 15 25 25 23 27 5 27 25 49
N             25 25 25 25 25 15 25 25 25 25 25
P              25 25 21 23 15 23 25 23 21 25
Q               29 21 25 15 15 25 25 21 15
R                    33 25 25 25 15 23 25 31 25 25
S                     675 25 25 25 25 115 25 25
T                  15 25 55 35 25 25
U                   15 27 21 21 25
V                    25 33 25 25
W                     33 25 45
X                      23 65
Y                       25
Z                       

Last revised 2024-04-14.

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Col. George Sicherman [ HOME | MAIL ]