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Hexomino corral


If a domino is two squares joined at a common edge, then a hexomino is a similar plane figure comprising six squares. Since a cube has six square sides, it follows that certain hexominos can be folded into a cube. Here is one: Col 173

| |
=== =|= ==|

==== + ===+
=== =| ===|
==== + ===+
==== | ===|
=== =+----+

There are others, of course. So this puzzle has two(+) parts.

  1. Count them.
    Counting as a single hexomino all shapes that differ only by rotation
    and/or reflection, sketch all the hexominos that will fold into a cube.
    How many are there?

  2. Corral them.
    Now fit them, without overlap, inside a rectangle or square.
    What is the smallest perimeter of that enclosure?
    Extra credit: what is the smallest area of that enclosure?

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