Pentacube Oddities with Dual Diagonal Symmetry
Introduction
A pentacube is a solid made of five cubes joined
face to face.
An oddity (or Sillke Figure)
is a figure with even symmetry
formed by an odd number of copies of a polyform.
Polycubes have 33 symmetry
classes (including asymmetry),
and 31 of them have even order.
That is too many to show here.
Instead I show only oddities with dual diagonal mirror symmetry.
In all pictures, the cross-sections are shown from top to bottom.
If you find a smaller solution, please write.
For other classes of symmetry, see:
Dual Diagonal Mirror Symmetry
Dual diagonal mirror symmetry is mirror symmetry through two different
plane diagonal axes.
The smallest example of a polycube with dual diagonal mirror
symmetry and no stronger symmetry
is this hexacube, found by W. F. Lunnon:
Achiral Pentacubes
The solutions for pentacubes
I and
X
are trivial.
Those pentacubes already have dual diagonal mirror symmetry.
The solution for pentacube
W
is a minimal solution for the W pentomino.
No smaller solution is known.
Chiral, Disallowing Reflection
Chiral, Allowing Reflection
Last revised 2024-02-15.
Back to Polyform Oddities
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Polyform Curiosities
Col. George Sicherman
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