Cell Shifts for Pentahex Pairs

Introduction

One figure can be tiled with one pentahex, and another figure can be tiled with another pentahex. The figures differ in only one cell. How near can the unmatched cells lie?

Here I show minimal shift vectors for pairs of pentahexes. The only unsolved case is I+T. (The I and T pentahexes are also probably not compatible. For compatibility results, see Pentahex Compatibility.)

If you find a smaller solution for any of these pairs, please let me know.

Summary

 ACDEFHIJKLNPQRSTUVWXYZ
A*1:41:11:21:21:11:31:21:21:21:21:21:41:11:61:81:51:21:81:41:21:3
C1:4*1:4√3:41:11:31:191:31:21:11:11:2√3:21:3√3:12√3:11:31:51:41:331:51:2
D1:11:4*1:41:41:41:41:21:21:21:11:11:11:21:51:71:11:31:21:51:31:2
E1:2√3:41:4*1:11:31:41:31:31:21:21:1√3:11:1√3:2√3:61:41:91:41:41:11:3
F1:21:11:41:1*1:21:61:11:21:31:11:11:31:31:21:31:21:71:31:41:11:1
H1:11:31:41:31:2*1:91:31:11:31:11:11:11:11:31:11:31:81:21:31:41:2
I1:31:191:41:41:61:9*1:51:61:11:31:21:81:45:5?1:31:61:35:351:31:2
J1:21:31:21:31:11:31:5*1:11:21:21:11:41:11:41:41:11:11:41:71:31:2
K1:21:21:21:31:21:11:61:1*1:21:21:21:21:11:11:21:31:31:11:11:11:2
L1:21:11:21:21:31:31:11:21:2*1:21:21:31:21:11:31:21:31:31:61:11:1
N1:21:11:11:21:11:11:31:21:21:2*1:11:21:21:31:31:31:21:31:31:11:2
P1:21:21:11:11:11:11:21:11:21:21:1*1:21:11:21:71:21:21:21:31:21:2
Q1:4√3:21:1√3:11:31:11:81:41:21:31:21:2*1:1√3:2√3:11:11:51:21:11:31:2
R1:11:31:21:11:31:11:41:11:11:21:21:11:1*1:31:11:31:31:41:31:21:2
S1:6√3:11:5√3:21:21:35:51:41:11:11:31:2√3:21:3*√3:31:21:31:15:51:31:2
T1:82√3:11:7√3:61:31:1?1:41:21:31:31:7√3:11:1√3:3*1:31:31:82√3:601:11:2
U1:51:31:11:41:21:31:31:11:31:21:31:21:11:31:21:3*1:61:61:11:71:2
V1:21:51:31:91:71:81:61:11:31:31:21:21:51:31:31:31:6*1:11:411:31:1
W1:81:41:21:41:31:21:31:41:11:31:31:21:21:41:11:81:61:1*1:31:41:1
X1:41:331:51:41:41:35:351:71:11:61:31:31:11:35:52√3:601:11:411:3*1:31:6
Y1:21:51:31:11:11:41:31:31:11:11:11:21:31:21:31:11:71:31:41:3*1:1
Z1:31:21:21:31:11:21:21:21:21:11:21:21:21:21:21:21:21:11:11:61:1*

Shifts

Shift 1

One Tile

Two Tiles

Three Tiles

Four Tiles

Five or More Tiles

Shift √3

Shift 2√3

Shift 5

Last revised 2016-05-01.


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Col. George Sicherman [ HOME | MAIL ]