# 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 ]