Minimal Oddities for the L Tricube

Introduction

A tricube is a solid made of three equal cubes joined face to face. There are two forms of tricube: the straight or I tricube, and the right or L tricube.

Polycubes can belong to any of 33 symmetry classes, including asymmetry; see Polycube Symmetries. Of these symmetry classes, 31 have even order and can be symmetries of oddities.

Here I show minimal oddities for the L tricube that belong to every even symmetry class. The minimal oddities of the I tricube are not interesting. They include only the tricube itself and the 3×3×3 cube.

If you find a smaller example for any symmetry class, please write.

For pentacubes, see Pentacube Oddities with Full Symmetry and Pentacube Oddities with Inverse Symmetry.

Solutions

The symmetry codes are those of W. F. Lunnon; see Polycube Symmetries. The order of a symmetry is shown next to its code. An asterisk means that the figure is unique for its number of tiles.

C4 2 *B6 2CF6 2 *F5 2 *
E4 2 *A12 4 *J10 4 *BC10 4
BB10 4CK6 4 *BE4 4CE3 4 *
BF6 4 *EE4 4CD10 6FF4 6 *
H12 6 *AB16 8 *EF6 8 *BFF8 8
CJ6 8 *AE8 8 *EFF7 8 *EEE6 8 *
BD34 12 *DF6 12 *BBC2 16 *R56 24 *
CCC20 24 *DEE25 24 *G1 48 *

Last revised 2022-12-17.

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Col. George Sicherman [ HOME | MAIL ]