Isolated 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, and separating the copies of the second pentahex.

See also

  • Pentahex Pair Hex-Convex Shapes
  • Tiling a Hex-Convex Polyhex with a Polyhex
  • Nomenclature

    Table of Results

     Isolated Pentahex
     ACDEFHIJKLNPQRSTUVWXYZ
    A6326066945441010662254333129
    C21662410612
    D62399326433633839328
    E24884224814863961414742041010
    F613412133015129141820101230
    H122233464612301427815
    I11603137884184146444334361166418
    J4241561046448461448
    K44642033181041882049
    L4638712358467710108711846
    N363478436344896969338
    P343356344334437464536
    Q412415412586612662204
    R363334401682068106472
    S3333
    T
    U6662141553
    V9186215810101417866183291188417415
    W69483093
    X332056384
    Y76284123394537331084756
    Z610149469844414644

    Navigation

    [2 Tiles] [3 Tiles] [4 Tiles] [5 Tiles] [6 Tiles] [7 Tiles] [8 Tiles] [9 Tiles] [10 Tiles] [11 Tiles] [12 Tiles] [13 Tiles] [14 Tiles] [15 Tiles] [16 Tiles] [17 Tiles] [18 Tiles] [20 Tiles] [21 Tiles] [22 Tiles] [24 Tiles] [25 Tiles] [27 Tiles] [29 Tiles] [30 Tiles] [33 Tiles] [36 Tiles] [40 Tiles] [41 Tiles] [43 Tiles] [44 Tiles] [46 Tiles] [48 Tiles] [54 Tiles] [56 Tiles] [58 Tiles] [60 Tiles] [66 Tiles] [72 Tiles] [74 Tiles] [78 Tiles] [84 Tiles] [93 Tiles] [118 Tiles] [141 Tiles] [225 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

    11 Tiles

    12 Tiles

    13 Tiles

    14 Tiles

    15 Tiles

    16 Tiles

    17 Tiles

    18 Tiles

    20 Tiles

    21 Tiles

    22 Tiles

    24 Tiles

    25 Tiles

    27 Tiles

    29 Tiles

    30 Tiles

    33 Tiles

    36 Tiles

    40 Tiles

    41 Tiles

    43 Tiles

    44 Tiles

    46 Tiles

    48 Tiles

    54 Tiles

    56 Tiles

    58 Tiles

    60 Tiles

    66 Tiles

    72 Tiles

    74 Tiles

    78 Tiles

    84 Tiles

    93 Tiles

    118 Tiles

    141 Tiles

    225 Tiles

    Last revised 2025-08-26.


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    Col. George Sicherman [ HOME | MAIL ]