# Pentahex Compatibility

## Introduction

A pentahex is a figure made of five regular hexagons joined edge to edge. There are 22 such figures, not distinguishing reflections and rotations.

Dr. Erich Friedman's Math Magic for September 2004 shows compatibility figures for pairs of pentahexes (and many other polyforms). Here are minimal known compatibility figures for pairs of pentahexes. Joe DeVincentis and Dr. Friedman found many solutions. Dr. Andrejs Cibulis was the first to solve some of the hardest compatibilities.

For compatible pairs of pentahexes with an odd number of tiles, see Pentahex Odd Pairs.

• Minimal Solutions
• Holeless Variants

## Minimal Solutions

ACDEFHIJKLNPQRSTUVWXYZ
A*422223222223266628323
C4*332392222222223233032
D23*3332222222226232322
E233*3224222222233182222
F2233*29222223222262662
H23322*102222223223112362
I3922910*38232835?18353522
J2224223*22222223223322
K22222282*2222222332222
L222222222*222222222823
N2222223222*23233222322
P22222222222*2236222222
Q322232822232*222642222
R2222233222222*22324222
S62222252223322*22341522
T626322?32236222*3266022
U63232318232226323*627862
V2231861132322242326*102422
W8322225322222446210*662
X3303263353283222156078246*24
Y23226622222222226262*2
Z322222222322222222242*

## Holeless Variants

In the table, green figures indicate solutions that are minimal even without the condition of holelessness. Below I show only holeless solutions that differ from those shown above.

ACDEFHIJKLNPQRSTUVWXYZ
A*?22229222223212??68324
C?*14102910232239222363?103
D214*333222222222?232322
E2103*32282322228??182222
F2233*31023222323?2122682
H29323*102222223823162362
I910221010*610232885??55?22
J2228226*222223232212322
K232232102*22222215332222
L222322222*222222422823
N2222223222*233322242322
P23222222222*223?222222
Q392232822232*222642224
R2222238322322*52326422
S122283852223325*?2314?22
T?2???2?315222?22?*32??2?
U?32?23?234226323*10??62
V663181216523242423210*10?22
W83222251222222614??10*662
X3?3263?3283224????6*24
Y210228622222222226262*2
Z432222222322422?22242*

### 22 Tiles

Last revised 2016-05-12.

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Col. George Sicherman [ HOME | MAIL ]