This plug-in (pronounced 'Boo-lee-ahn', or ブーリアン in Japanese), lets you combine two objects in various ways. The Boolean plugin should be included with Metasequoia shareware version and the free LE version when downloaded from the official website. However, you still must have a registered version of Metasequoia to use any plugin. If it doesn't show up under Menu --> Object --> Boolean (or ブーリアン) with a registered copy, one may have to search Google for them, though the original creator's site gives a 500 Error when one attempts to access the boolean plug-in page. There is also an unofficial English translation for Boolean.

An article posted on the Blogspot blog Cut, Fold & Paste here, gives an in-depth explanation of each of the eight options available in this plug-in. The writer focuses on Pepakura modeling, so the article mentions the 'usefulness' of each option relative to its use in Pepakura. Still, a very helpful and clearly-explained tutorial copy-and-pasted here, without any editing:

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Metasequoia's Boolean pluginEdit

I'm going talk a bit about Metasequoia's Boolean plugin.
Before you continue reading, please note that the plug-in function is only available to registered copies of Metasequoia. If you have the LE or the unregistered Shareware version, you won't be able to use the Boolean plugin.
Okay, let's start.
First things first, the boolean plugin is not UNICODE compliant. This means that even if you've got East Asian language support installed in your OS, you will still see garbage characters when you run the plugin. The only way to properly 'see' the Kanji characters on this plugin is to configure your OS to treat non-Unicode characters as SJIS. Assuming you do this configuration correctly, here's how the Boolean dialog box should look like:
[1] Lots of options! But for this tutorial, you should only pay attention to the three combo boxes. The left and right most combo boxes are the operands. These combo boxes will be populated by the objects you've defined in Metasequoia. The middle combo box is the operator. This contains the boolean operations that you can perform.
The "OK" button starts the boolean operation. (By the way, the "OK" button should be legible even if you're running an English only OS.)
The button to the right of the "OK" button is the Cancel button. On English OS'es, this appears as "??????".
The bottom left most button ("?") brings up the help dialog box. On English OS'es, you'll get a dialog box with garbage characters. But if you did the configuration I mentioned earlier, here's what you'll get:
[2] Again, lots of options! If I have the time, maybe I'll pull out my Kanji dictionary and try to translate all of them. (Sigh... if only the text on that dialog box were selectable, I could have run them through Google translate...)
Anyway, the options you should pay attention to are the following:
[3] These are the options that will be available in the Operations combo box that I identified earlier. I labeled the options with numbers so you'll know what entry they are in the Operations combo box, since they'll be illegible when running in English mode.
Now, let's run through each operation.
For my example, I'll be using the following objects:
[4]In the screenshot above, I defined two objects, namely "Red" and "Blue".

1. UNION (Red + Blue) This is the 1st option in the Operations combo box.
The Union operation creates a new object by joining objects Red and Blue. The name of the new object will be "Red+Blue".
Here's how the results look like:
[5]I intentionally hid the surfaces so you can see how the two objects are joined.
2. SUBTRACT (Red - Blue) This is the 2nd option in the Operations combo box.
The Subtract operation carves out from Red the area occupied by Blue. The name of the new object will be "Red-Blue".
Here's how the result looks like:

[6] 3. NOT ( Red ! Blue ) This is the 3rd option in the Operations combo box.
This operation is almost similar to the Subtract operation. Basically, it performs a Union of Red and Blue. Afterwards, it removes the surfaces of Blue. The name of the new object will be "Red!Blue".
Here's the result:
[7]Note that unlike the Subtract operation, this operation does not patch up surfaces removed.
4. AND ( Red & Blue ) This is the 4th option in the Operations combo box.
This operation creates a new object that contains the area where Red intersects with Blue. The name of the new object will be "Red&Blue". However, since the Windows UI treats the "&" character as a menu accelerator, the object name will appear as "RedBlue" in the object list.
Here's the result:
[8] 5. INTERSECT ( Red # Blue ) This is the 5th option in the Operations combo box.
This operation marks out in Red where the surfaces of Blue intersects with it. The name of the new object will be "Red#Blue".
To better illustrate, here's the result:
[9] 6. ???? (????) This is the 6th option. This option is bugged. Calling this option produces the same results as INTERSECT, but the name of the object is based on the AND operation... weird...
In other words, if I do a Red % Blue, I'll get a new object that looks like the result of Red # Blue, but is named as "RedBlue".
7. ASTERISK ( A * B ) This is the 7th option in the Operations combo box.
This is an interesting operation which I've yet to find something useful for. :)
What this does is it creates a new object where object A replaces every node that object B has.
To illustrate, I start with the following:
[10]The sphere is Obj1, while the cube is Obj2.
After performing the operation, here's the result:
[11]Interesting eh? But again, for the purpose of Card Model creation, I've yet to find any useful applications for this operation.
8. DOUBLE ASTERISK ( A : B ) Hahahah.. okay... the word, "COLON" just doesn't sound pleasant. So let's just use double asterisk.
This is the last option in the Operations combo box.
This basically does what the Asterisk operation does. However, this does an extra step of "connecting" each just look at the example below.
Let's say we've got the following objects:
[12] Obj1 is the red sphere, while Obj3 is the green shape.
After performing the operation, here's the result:
[13] Ewww... what a mess! Like its sibling, the Asterisk operation, this is really useless for Card Modeling.
It might be useful if you want to make jackstones or a model of a Spathi Eluder ship from the StarCon2 game. :)

Finally, if you're a bit adventurous, you can check out the button at the upper left corner of the Boolean dialog box. This allows you to manually enter a boolean like "C=Red+Blue".
Anyway, I hope you've found this short tutorial helpful.

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Notes on Metasequoia 4.xEdit

When Meta 4.x came out, the Boolean Plugin has been removed and replaced with native BOOLEAN support!  Since everything is natively coded, the quality and accuracy of the boolean operations have been dramatically improved.

However, some of the operations available in the old 3.x plugin are no longer available.

Here's a list of the boolean operations that you can do in Meta 4.x

  • UNION (A + B) : Same as 3.x.
  • SUBTRACTION (A - B) : Same as 3.x, but quality vastly improved, but not perfect.  Gone are the days when you get a lot of weird, orphaned vertices and faces as in 3.x.  This time around, the SUBTRACT operation produces a really clean output with very little "trash" or orphaned edges.
  • INTERSECTION (A ∩ B) : Same as 3.x and like SUBTRACTION, vastly improved quality.

Example of use:

Boolean 1

Boolean 2