Tiling a Triangle with a Pentiamond and a Heptiamond

Introduction

A pentiamond is a plane figure formed by joining 5 equal equilateral triangles edge to edge. There are 4 pentiamonds:

A heptiamond is a plane figure formed by joining 7 equal equilateral triangles edge to edge. There are 24 heptiamonds:

Which pairs of a pentiamond and a heptiamond can tile a triangle? Here I show some minimal tilings of triangles by copies of a pentiamond and a heptiamond.

Please write if you solve an unsolved pair.

Carl Schwenke and Johann Schwenke contributed many new or improved solutions.

Table

This table shows the side lengths of the minimal known triangles.

 7A7B7C7D7E7F7G7H7I7J7K7L7M7N7P7Q7R7S7T7U7V7X7Y7Z
5I 121066111569699996146126919161499
5J ?12????666?966??15????????
5Q 61612627121216910?111066?6??126?106
5U ??????61618??66???????????

Side 6

Side 9

Side 10

Side 11

Side 12

Side 14

Side 15

Side 16

Side 18

Side 19

Side 27

Last revised 2025-03-16.

Back to Tiling a Triangle with Two Polyiamonds < Polyiamond and Polyming Tiling < Polyform Tiling < Polyform Curiosities
Col. George Sicherman [ HOME | MAIL ]