Pentahex Pair Hex-Convex Shapes

Introduction

A polyhex is said to be hex-convex if every line joining the centers of two of its cells lies in its interior. Here are the smallest known hex-convex polyhexes that can be formed with copies of two pentahexes, using at least one of each.

See also Tiling a Hex-Convex Polyhex with a Polyhex.

Nomenclature

Table of Results

 ACDEFHIJKLNPQRSTUVWXYZ
A632630644433461264246141356
C6242612181356644618466610
D323693243334338539328
E24234644654364271264126458
F6664121318206751215422010418
H3012961218141266278129
I618341318101434318141523856248839
J413524181410553444666838
K46462014546412645
L46356123543367810664844
N343476436334696969334
P343356344334437464534
Q46461218464412264
R61834152714412764126616141312
S1263271589333
T4281262386610672910
U4454856694266536
V663124212664666663296241744
W141696202449416246
X334108888351415175
Y5625493354334331034654
Z61088189844412644

Navigation

[2 Tiles] [3 Tiles] [4 Tiles] [5 Tiles] [6 Tiles] [7 Tiles] [8 Tiles] [9 Tiles] [10 Tiles] [12 Tiles] [13 Tiles] [14 Tiles] [15 Tiles] [16 Tiles]
[17 Tiles] [18 Tiles] [20 Tiles] [24 Tiles] [27 Tiles] [29 Tiles] [30 Tiles] [42 Tiles] [66 Tiles] [88 Tiles] [126 Tiles] [135 Tiles] [141 Tiles] [238 Tiles]

Solutions

These minimal known solutions are not necessarily unique.

2 Tiles

3 Tiles

4 Tiles

5 Tiles

6 Tiles

7 Tiles

8 Tiles

9 Tiles

10 Tiles

12 Tiles

13 Tiles

14 Tiles

15 Tiles

16 Tiles

17 Tiles

18 Tiles

20 Tiles

24 Tiles

27 Tiles

29 Tiles

30 Tiles

42 Tiles

66 Tiles

88 Tiles

126 Tiles

135 Tiles

141 Tiles

238 Tiles

Last revised 2025-08-18.


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Col. George Sicherman [ HOME | MAIL ]