Pentacube Oddities with Ternary/Diagonal Mirror 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. Here I show oddities with ternary/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 Polycube Oddities.

Ternary/Diagonal Mirror Symmetry

Ternary/diagonal mirror symmetry is mirror symmetry through a plane diagonal axis combined with 120° rotation around a solid diagonal axis.

The smallest example of a polycube with ternary/diagonal mirror symmetry and no stronger symmetry is the K tetracube:

Achiral Pentacubes

Chiral Pentacubes

Last revised 2026-09-05.

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Col. George Sicherman [ HOME | MAIL ]