Baiocchi Figures for Pentiamond-Hexiamond Pairs

Introduction

A pentiamond is a plane figure formed by joining 5 equilateral triangles edge to edge. A hexiamond is a plane figure formed by joining 6 equilateral triangles edge to edge.

Here I show the smallest polyiamond with full symmetry that can be tiled by a pentiamond and a hexiamond, using at least one copy of each. The solutions shown are not necessarily uniquely minimal.

Basic Solutions

5I+6A : 66	5J+6A : 54	5Q+6A : 66	5U+6A : 36

5I+6E : 66	5J+6E : 42	5Q+6E : 66	5U+6E : 42

5I+6F : 48	5J+6F : 48	5Q+6F : 54	5U+6F : 48

5I+6H : 48	5J+6H : 42	5Q+6H : 66	5U+6H : 48

5I+6I : 54	5J+6I : 48	5Q+6I : 42	5U+6I : 66

5I+6L : 48	5J+6L : 42	5Q+6L : 48	5U+6L : 66

5I+6O : 48	5J+6O : 42	5Q+6O : 36	5U+6O : 36

5I+6P : 54	5J+6P : 48	5Q+6P : 54	5U+6P : 66

5I+6S : 66	5J+6S : 42	5Q+6S : 48	5U+6S : 66

5I+6U : 66	5J+6U : 42	5Q+6U : 48	5U+6U : 48

5I+6V : 42	5J+6V : 48	5Q+6V : 48	5U+6V : 48

5I+6X : 54	5J+6X : 66	5Q+6X : 66	5U+6X : 48