Tiling a Polyomino at Scale 2 with Two Hexominoes

  • Introduction
  • Table
  • Solutions
  • Holeless Variants

    • Introduction

    A hexomino is a figure made by joining six squares edge to edge. There are 35 such figures, not distinguishing reflections and rotations.

    Here I study the problem of arranging copies of two hexominoes to form some polyomino that has been scaled up by a factor of 2.

    If you find a smaller solution, or solve an unsolved pair, please write.

    See also

  • Tiling a Polyomino at Scale 2 with a Hexomino
  • Tiling a Polyomino at Scale 2 with a Pentomino
  • Tiling a Polyomino at Scale 2 with Two Pentominoes
  • Tiling a Polyomino at Scale 2 with a Tetromino and a Pentomino
  • Tiling a Polyiamond at Scale 2 with Two Hexiamonds
  • Tiling a Polyabolo at Scale 2 with Two Tetraboloes

    • Table of Results

    This table shows the smallest total number of copies of two hexominoes known to be able to tile some polyomino enlarged by a scale factor of 2, using at least one copy of each hexomino.

     1234567891011121314151617181920212223242526272829303132333435
    1 •48106444168666610616102824818228822202868427824??
    2 4•8848484484668688121248441046444410101616
    3 88•8812612810466612466840641264848610616166456
    4 1088•444640?168488?8640??1416??8?8?446????
    5 6484•646861024884104614464488864648181016
    6 4812446•4?1816166101088166414?432816?96??61646496??
    7 446644•464844684846184644868646261888
    8 4812406?4•?8?61414?16????8??8????4164????
    9 1648?8186?•16?8126?8?16??6??2440?8?1248????
    10 8410166164816•4046456616632?61616440161618610412???
    11 684810168??40•848?882440?128?10168168818840???
    12 64642646848•468610610124664888864410121216
    13 666841041412644•4446108166488888104844888
    14 666881061464864•868148648124141281464688816
    15 10812?8888??56?848•4840??816?88?32?8328????
    16 66484164168686464•812868161862488164848122472
    17 168661068??168106888•1616?4??241612163866148243256
    18 108640444?1662461014401216•??81688?16??884????
    19 28128?6146??32401088?816?•?1488??????888????
    20 241240?14?18????12166?6???•10???????16??????
    21 846144448661246488481410•128881681048416161616
    22 1884166326??1686481616?1688?12•?16?81681412812?3232
    23 22412?484??16?6812?18?8??8?•?????644????
    24 846?416482441048486248??816?•8?8?824????
    25 810488?8?404016881482416???8??8•?16?8168????
    26 2248?8966??1688812?81216??168???•??1048????
    27 206488?8?8161688832816???816?816?•?2488????
    28 2848?6?6??18881014?1638???108?????•888????
    29 646446441268646846881641468810248•641616616
    30 8410461661641018484328688?81242164886•4816??
    31 44664424848446841448?4844888844•8128368
    32 2781016?8646??12401048?88???1612??????1688•???
    33 241016?189618????1288?1224???16???????1616128?•??
    34 ?1664?10?8????1288?2432???1632??????6?36??•?
    35 ?1656?16?8????16816?7256???1632??????16?8???•
     1234567891011121314151617181920212223242526272829303132333435

    Solutions

    So far as I know, these solutions use as few tiles as possible. They are not necessarily uniquely minimal.

    2 Tiles

    4 Tiles

    6 Tiles

    8 Tiles

    10 Tiles

    12 Tiles

    14 Tiles

    16 Tiles

    18 Tiles

    20 Tiles

    22 Tiles

    24 Tiles

    28 Tiles

    32 Tiles

    36 Tiles

    38 Tiles

    40 Tiles

    44 Tiles

    56 Tiles

    64 Tiles

    72 Tiles

    88 Tiles

    96 Tiles

    128 Tiles

    278 Tiles

    Last revised 2026-04-21.

    Back to Polyomino and Polyking Tiling < Polyform Tiling < Polyform Curiosities
    Col. George Sicherman [ HOME | MAIL ]