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.

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.

  ABCC′EE′FHH′IJJ′KLMNPQRR′SS′TUVWXYZ
A 15212121212121212121212121152125212121272521
B  332125192121232123212121212323152121172323
C   –192525333355252525252721212133153333512525145–2555
E     212523232521211521112121212121252525152121252125
F     332521252525252525252525152525232525
H        332515252525252525332929252525152125312525
I       2525255252325252525252525252525
J           211521112121212525152525152125252125
K         2125212121255125252525252525
L          21252521252525212525252125
M           17172515252523275272551
N            2525252525152525252525
P             25252123152325232125
Q              292125151525252115
R                   33252525152325312525
S                     675252525251152525
T                 152555352525
U                  1527212125
V                   25332525
W                    452545
X                     2365
Y                      25
Z                       

Last revised 2020-11-08.

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Col. George Sicherman [ HOME | MAIL ]