Triquoin Oddities

Introduction

A triquoin is a solid made of three equal cubes joined at faces, half faces, or quarter faces. There are 35 triquoins, or 54 if mirror images are distinguished. Triquoins were first defined and enumerated by John Mason. See Catalogue of Polyquoins.

An oddity (or Sillke Figure) is a figure with even symmetry formed by an odd number of copies of a polyform.

Like polycubes, polyquoins have 33 symmetry classes (including asymmetry). Of these classes, 31 have even order. Here I use any convenient symmetry classes of even order. With one exception, these oddities are known to be minimal. Not all are uniquely so.

In constructing the oddities, the triquoins are not reflected. This is customary when working with solid shapes.

If a triquoin has distinct mirror forms, only one appears here.