Pentahex Odd Pairs

  • Introduction
  • Summary
  • Solutions
  • Holeless Variants
  • 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.

    Pentahex Compatibility shows minimal known compatibility figures for pairs of pentahexes. Here are minimal known compatibility figures with an odd number of tiles.

    For odd compatibility figures for pairs of pentominoes, see Livio Zucca's Pentomino Odd Pairs.

    A convenient set of acrylic pentahexes (and smaller polyhexes) is available from Kadon Enterprises as Hexnut.

    Summary

    I adopt Dr. Friedman's nomenclature:

    In the table below, green figures denote solutions that are minimal even without the condition that the number of tiles be odd.

     ACDEFHIJKLNPQRSTUVWXYZ
    A*9333333333333913939333
    C9*333393333333333333933
    D33*333533333333151535333
    E333*3737333333933153337
    F3333*393333333373133973
    H33373*133333333733113373
    I3953913*3133371135?27353535
    J3337333*33333333333333
    K333333133*3333333333333
    L333333333*3333337331333
    N3333333333*33333337333
    P33333373333*3339733333
    Q3333331133333*373793335
    R3333333333333*33337333
    S93393753333373*333111533
    T13315373?33339333*33158733
    U931533327337377333*998193
    V33315131133333393339*113933
    W935333533373371115911*773
    X33933933533133333158781397*39
    Y33337733333333339373*3
    Z333733533333533333393*

    Solutions

    3 Tiles

    5 Tiles

    7 Tiles

    9 Tiles

    11 Tiles

    13 Tiles

    15 Tiles

    27 Tiles

    35 Tiles

    39 Tiles

    81 Tiles

    87 Tiles

    Holeless Variants

    Last revised 2023-05-07.


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    Col. George Sicherman [ HOME | MAIL ]