Polycube Oddities

Introduction

A polycube is a solid geometric figure formed by joining equal cubes face to face. A polycube oddity is a solid with symmetry of even order, formed by joining an odd number of congruent polycubes.

This page shows minimal known oddities for various polycubes with various symmetries.

Specific Polycubes

Minimal Oddities for the L Tricube. Oddities for the L tricube with every even polycube symmetry.
Minimal Oddities for the L Tetracube. Oddities for the L tetracube with every even polycube symmetry.
Minimal Oddities for the P Pentacube. Oddities for the P pentacube with every even polycube symmetry.

Specific Symmetry Classes for General Pentacubes

2-Fold Symmetry

Pentacube Oddities with Orthogonal Mirror Symmetry.
Pentacube Oddities with Diagonal Mirror Symmetry.
Pentacube Oddities with Orthogonal Rotary Symmetry.
Pentacube Oddities with Plane Diagonal Rotary Symmetry.
Pentacube Oddities with Inverse Symmetry.

4-Fold Symmetry

Pentacube Oddities with Orthogonal/Diagonal Symmetry.
Pentacube Oddities with 4-Rotary Symmetry.
Pentacube Oddities with Dual Orthogonal Mirror Symmetry.
Pentacube Oddities with Dual Diagonal Mirror Symmetry.

8-Fold Symmetry

Pentacube Oddities with Square Symmetry.

16-Fold Symmetry

Pentacube Oddities with Square Box Symmetry.

48-Fold Symmetry

Pentacube Oddities with Full Symmetry.

Full Symmetry for Pairs of Polycubes

Pentacube Pair Full Oddities. Full-symmetry oddities formed by copies of two pentacubes.
Tetracube-Pentacube Pair Full Oddities. Full-symmetry oddities formed by copies of a tetracube and a pentacube.
Back to Polyform Oddities < Polyform Curiosities
Col. George Sicherman [ HOME | MAIL ]