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Making Polyhedra From (Magic) Cards: A Guide - With Templates
Jack van Riel
Netherlands
Tilburg
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Thanks for all the comments, compliments and geekmails!

Many people have asked me how to make these 'magical spheres'. This geeklist explains the process, and provides templates so you can make the structures yourself.

Note that although there is a lot of math behind these polyhedra, I am no mathematician. My method was 50% calculations and 50% trial and error. I didn't always bother to find the exact length or angle; if it fit and looked nice, it was good enough for me.
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1. Board Game: Magic: The Gathering [Average Rating:7.44 Overall Rank:123]
Jack van Riel
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Step one: Find a Polyhedron

The first thing you need to do is to find a suitable polyhedron to base your structure on. (Obviously, if you copy my templates, you can skip the first steps.)

This is not actually that easy. I wanted a polyhedron with all identical faces, so all cards could be cut the same. Many polyhedra have triangle- or pentagon-shaped faces, that don't translate well to the rectangle-shaped cards. A shape that does work well, is the rhombus (diamond).

Let's say we pick the rhombic triacontahedron (known to RPG'ers as a D30) as our polyhedron. It has 30 rhombus-shaped faces and looks like this (thanks wikipedia!):
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2. Board Game: Magic: The Gathering [Average Rating:7.44 Overall Rank:123]
Jack van Riel
Netherlands
Tilburg
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Step two: Fit the Cards

From our chosen polyhedron we know that we need 30 cards; one for each face. It's like we're glueing the cards onto the polyhedron, only our cards will be held together because they interlock; no need for glue!

There are several ways you could fit the cards onto the rhombus-shaped faces. You could do it like this:

However, this is problematic. Placed this way, the cards are much bigger than the faces of the polyhedron. This means that at the sharp points you'll have five intersecting cards. Too difficult, let's look at another option:

Here the points touch the card edges. This means that five cards will meet there, but won't intersect eachother. My 'red' polyhedron is made this way. It is relatively hard to build, though. This is because the cards cover the entire structure. I would not recommend you try to build that one as your first. We can make it easier if we place the cards like this instead:

You can see that the card doesn't cover the whole rhombus. This means there will be holes in the final structure. This makes building it a lot easier, and it will still be really strong (and pretty, too!)
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3. Board Game: Magic: The Gathering [Average Rating:7.44 Overall Rank:123]
Jack van Riel
Netherlands
Tilburg
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Step three: Create a Template

To create a template, we go from this:

to this:

to this:

The thick black lines are where you'll have to cut the cards.

See how it works? We cut each card on the edges of the rhombus. But instead of cutting all the way through, we make two cuts a part of the length from both sides, so two cards can slide together there.
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4. Board Game: Magic: The Gathering [Average Rating:7.44 Overall Rank:123]
Jack van Riel
Netherlands
Tilburg
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Step four: Make a Three Card Lock

Now that we have our 30 cards cut according to our template, we must slide them together. This is the hard part. If you can do this, the rest will be easy. We need to create a lock from three intersecting cards.

First, slide two cards together, like this. Note that you always line up a cut in the short edge from one card with a cut in the long edge from another.

After sliding the two cards together, we have to fit the third one in. It's a lot easier if you view it from the back, or what will be the inside of the eventual structure. The edges will bend towards you, the middle away from you.

In the next picture I've tried to show how you need to pull a corner of the third card through a small cut in the second card. This isn't easy. You'll have to slide and bend the cards quite a bit. Luckily magic cards are strong and won't easily tear.

You'll probably have to twist and bend the cards on the other side too, to get them to fit nicely together.

If you manage to do it, the three card lock will look like this when viewed from the inside:

This step is hard. Keep trying, you'll get it. How to make this lock is all you need to know to create the different structures.
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5. Board Game: Magic: The Gathering [Average Rating:7.44 Overall Rank:123]
Jack van Riel
Netherlands
Tilburg
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Step five: Put the Polyhedron Together

This particular polyhedron is made entirely from three card locks. You now know how to do this, so this shouldn't be too hard. When finished, it will look like this:
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6. Board Game: Magic: The Gathering [Average Rating:7.44 Overall Rank:123]
Jack van Riel
Netherlands
Tilburg
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A Different Polyhedron

The structure in the picture to the left is made from 60 cards. The polyhedron it is based on has kite-shaped faces.

How do we do that? Like this:


Again, I made sure the card doesn't cover the kite completely, to avoid having four or five cards intersect. This polyhedron is probably easier to build, as there are three card locks on only one end of each card.
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7. Board Game: Magic: The Gathering [Average Rating:7.44 Overall Rank:123]
Jack van Riel
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Tilburg
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More Templates

The Red one (30 cards):

The White one (12 cards):
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8. Board Game: Magic: The Gathering [Average Rating:7.44 Overall Rank:123]
Jack van Riel
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And more...

The Black one (24 cards):

The Blue one (24 cards):

The blue sphere has four card locks, but the overlap is pretty small. A little harder than the others, maybe, but not much.
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9. Board Game: Magic: The Gathering [Average Rating:7.44 Overall Rank:123]
Jack van Riel
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Tilburg
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A Star

The 12, 24, 30 and 60 card spheres were all the possible sphere-like polyhedra I could find. So I made a star. Here's the template (60 cards):



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10. Board Game: Magic: The Gathering [Average Rating:7.44 Overall Rank:123]
Jack van Riel
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Tilburg
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Another Star

And I made another (60 cards):
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11. Board Game: Magic: The Gathering [Average Rating:7.44 Overall Rank:123]
Jack van Riel
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On the Internet

A number of people pointed me to this link: http://www.georgehart.com/cards/cards.html. Polyhedra made from playing cards. I especially like the computer renderings there.

I also found a lot of virtual models (and some real ones) of playing card polyhedra on flickr.

-----

Thanks for reading. If you make your own, please share! I'd love to see them.
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12. Board Game: Yu-Gi-Oh! Trading Card Game [Average Rating:5.75 Overall Rank:6885]
Martin Klein
Germany
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Nordrhein-Westfalen
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Hey, thanks for the templates!

I tried to make a Deltoidal Hexecontahedron with 30 Yu-Gi-Oh Cards (I don't own any magic cards, I guess I'm just too young. A friend of mine tried to convince me to play Yu-Gi-Oh once, but I have to say that I'm really not a fan of such trading card games, so it was no pain for me to cut these cards...)

I think I made a mistake somewhere, because in the end I only used 24 cards at all. I made 8 of these "three card locks" and then just put four of them together which gave me a half bowl.

Well, it was my first attempt and I have to admit that I didn't work very properly. I was just so curious to see how this would work. It took me a while to understand how to make those "three card locks", but then it suddenly worked and was quite simple, allthough a lot of "card-bending" was required.

If you look at my picture, you'll see that my work is not a patch on the original ones. Mine is just not so properly done and most of the cards are pretty much twisted.

The whole thing is really robust, we threw it around and played a little soccer with it and its still in an ok condition. The picture was taken after that, so this might also explain some of the dog-ears.

I think I will give it another try, Yu-Gi-Oh cards work fine for practise, but they are pretty ugly.

Thanks again to the OP for the templates, that was really interesting!

Viele Grüße, Martin
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