Polycube Oddities

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.

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.
Pentacube Oddities with Full Symmetry. Full-symmetric oddities for pentacubes.
Pentacube Oddities with Orthogonal Mirror Symmetry. Orthogonal mirror-symmetric oddities for pentacubes.
Pentacube Oddities with Diagonal Mirror Symmetry. Diagonal mirror-symmetric oddities for pentacubes.
Pentacube Oddities with Orthogonal Rotary Symmetry. Orthogonal rotationally symmetric oddities for pentacubes.
Pentacube Oddities with Plane Diagonal Rotary Symmetry. Plane diagonal rotationally symmetric oddities for pentacubes.
Pentacube Oddities with Inverse Symmetry. Point-symmetric oddities for pentacubes.
Pentacube Oddities with 4-Rotary Symmetry. Rotary 90° oddities for pentacubes.
Pentacube Oddities with Dual Orthogonal Mirror Symmetry. Rectangular-symmetric oddities for pentacubes.
Pentacube Oddities with Dual Diagonal Mirror Symmetry. Oblique rectangular-symmetric oddities for pentacubes.
Pentacube Oddities with Square Symmetry. Square (dual orthogonal + 4-rotary) oddities for pentacubes.
Pentacube Oddities with Square Box Symmetry. Dicubic (square-box) oddities for pentacubes.
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 ]