# Pentahex Pair Frame Tilings

## Introduction

A polyhex frame is a regular hexagonal polyhex with a centered regular hexagonal hole. Erich Friedman studied polyomino frame tilings in his Math Magic problem for January 2008. At my suggestion, he added frame tilings for polyiamonds and polyhexes.

On this page, for each pair of pentahexes, I show a frame tiling with the fewest known cells, using at least one copy of each pentahex of the pair. If you find a smaller solution or solve an unsolved case, please write.

## Table of Results

ACDEFHIJKLNPQRSTUVWXYZ
A12121218241212121212121212126902424114121218
C1212541212129012612121818246121212
D1212612121212126121212121212121218121212
E125461212181212121212181210814424618121818
F181212121812661812181212124266121218
H2412121218241212121218126612
I12121218122430241212122418423012541218
J12901212661230121212121812361212612
K121212121824126121218241212
L1266121212121261266618181212121266
N12121212181212121212612121212181218121212
P12121212121212121266612121212121212612
Q12181218122418612630181812
R1218121212181812186121230182418781212
S1261210842181212612
T90121443618121212618
U24122412302412181218181242181224
V242412642661212121212121824664242721212
W114618186654121812184212
X12121212121212121278187212
Y121212181212126126126121212181212121212
Z181212181818126121212241212

• 6 Tiles
• 12 Tiles
• 18 Tiles
• 24 Tiles
• 30 Tiles
• 36 Tiles
• 42 Tiles
• 54 Tiles
• 66 Tiles
• 72 Tiles
• 78 Tiles
• 90 Tiles
• 108 Tiles
• 114 Tiles
• 126 Tiles
• 144 Tiles

## 144 Tiles

Last revised 2024-07-13.

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Col. George Sicherman [ HOME | MAIL ]