No human language has the proper language for 3-D shapes. Like, it's really hard to describe abstract shapes JUST using words without using the phrase "It looks like a...."
Wouldn't that be a cool game? You are given a card with a drawing of an object on it (it could actually be a 3-D object, which is much better because it's harder)
And you'd have to describe this object in words. Like, "it's a cylinder, with a triangle-shaped notch cut out..." I dunno.
Then the person you're describing to has to draw the thing you're describing.. Or in the more challenging version, they'd have to shape it out of clay. Of course, this could be intensely challenging, or really easy depending on the complexity of the shape.
You could make it competitive, of course. Like which pair is better at describing the thing so their partner will be able to render it more perfectly without seeing it.
I have a 3-D object in my mind. I'm going to describe it in terms of shapes and geometry. You try to form a mental image of this thing. (If you're up for the CHALLENGE, WEAKLING!!!!)
For this game, you'll need to imagine a 3-D field. Imagine the X,Y and Z axis. Look as if you're standing at Z 10 or something (let's say that means 10 meters away), so that you see Z running under your feet, like rail road tracks into the distance.
Now, coming from left to right (crossing the Z line in the middle of your field of vision) is the X axis.
From the sky to the floor (crossing the Z line in the middle of your field of vision) is the y axis.
Now I'll describe the object to you. Listen up.
Imagine a solid cylinder that's wide and short, sitting on the floor, with the circle parts of the cylinder facing towards the ceiling and towards the ground. From the floor to the top, it's about as tall as half the diameter. So it's wider than it is tall.
Let's say it's one meter wide and half a meter tall.
Now, imagine making another object. This new object will become an appendage to the first object.
Let's use the workspace IN FRONT OF the object (that 10-meter area closer to you, along the z axis) to construct the new object
Start with a rectangular prism that's as tall as the cylinder.
It's about as wide as 1/4 of the cylinder and it's about as long as the cylinder's diameter.
In terms of meters, this rectangular prism is half a meter tall, 1 meter long (z-axis) and 1/4 meter wide (x-axis).
Now let's move this prism so that it touches the cylinder. Push it directly away from you (along the z axis), toward the original object, until the far wall of the appendage touches the curved wall of the cylinder. Now, along the x axis, push the appendage to the right until the right wall of the appendage is in line with the farthest right point in the circle of the cylinder. Now push it AGAIN directly away from you in the z plane, so that it touches the cylinder again. The far left corner of the appendage object should be making contact with the cylinder.
Now, pretend that it's all made of clay.
See how only the far left corner of the appendage is touching the cylinder? And just to the right of that point of contact is empty space? Fill in that empty space by extending the far right wall of the appendage away from you in the z plane until it touches the cylinder. Extend the top and bottom walls of the appendage away from you in the z plane until they touch the cylinder. Now, you have these two objects joined.
Since it's made of clay, blend walls together, to make these two objects into one. Smooth the walls out.
Therefore, the right side of the new whole object you've created should be totally flat and straight.
Looking to the left side of the appendage, where it touches the curved wall of the cylinder, blend the walls of the appendage (in the z plane) so that it forms a nice curve into the wall of the cylinder.
Now make the whole thing hollow. Hollow it out. Do it. Make the walls thin, only about 10 centimeters thick.
Since it's hollow, you can cut into it easily, like cutting into clay. Cut an opening from floor-to-ceiling of the closest-to-you wall of the appendage.
Start the incision 10 centimeters up from the floor, 10 centimeters in from the left wall. Run the incision upward in the y-plane, so it runs parallel to the wall of the object. Stop it about 10 centimeters down from the top of the object. Withdraw your knife and get ready to make another incision.
From the point you left off, move right on the x axis, until you're 10-cm from the RIGHT wall of this object. Make another such incision top-to-bottom here, parallel to the first incision.
Now you should have two incisions that run up and down and are parallel to each other.
Now, just make two more incisions that connect the ends of these two incisions. So you just cut out a thin rectangle. Throw this away, so there's a thin slit in the wall. If you look into this slit, you'll see the hollow interior of the object.
You know the part where the "appendage" touched the main cylinder? Delete these interior walls, so when you look into the slit, you can see all the way into the hollow body of the main cynlinder.
Put your knife safely away. Now run your hand along the right wall of the appendage in the z axis. Stop when you get to around the point where the appendage met the wall of the cylinder (even though you can't see the seam, because you blended it all out a minute ago, remember?)
Cut a slit here that runs the height of the object (in the y axis). The incision should start about 10 centimeters up from the floor, and stop about 10 centimeters down from the top of the object.
Now keeping moving on the z axis, until you're about even with the center of the circle. Make another such top-to-bottom incision here.
Now you should have two incisions that run up and down and are parallel to each other.
Now, just make two more incisions that connect the ends of these two incisions. So you just cut out another rectangle. Throw away the two rectangles you just cut out.
Go back to your original vantage point. You have just created an object that's hollow and has two long rectangular slits as openings. One of the slits is on the appendage, going up and down, on the wall that faces you. And the 2nd slit is along the right side of the object, also running up and down..
Now take the entire object and rotate it 90 degrees counter-clockwise around the z axis. The appendage should now be facing you still, but its long wall, which used to be the height, is now the width. The slit in this wall is still facing you, and it's now oriented horizontally. The second rectangular slit you cut is now facing up at the sky. Got it?
Now, take your viewing position from +10 on the z axis, and move to -10, and shift your view 180 degrees in the z plane. In other words, just view the object from behind.
From this vantage point, you're basically just going to add a small object to the butt-side of this thing. It's the shape of a torus (that's the geometric name for "donut") with the hole oriented in the x plane.
Now, the size of the torus:
The torus is about as tall as one third of the circle of the original cylinder. (So, like one third of a meter) It's thin; about the width of 1/5 of a meter.
Stick the edge of this torus to the direct back of the object, directly in the middle. Solder it on firmly.
Now go back to your original viewing position.
Make a sphere with a diameter about one fourth of the height of the object.
Put this sphere directly inside the hollow cavity in the center of the object.
Now shrink the whole thing down so it's about two inches long.
Turn all of it into steel.
Now you should know what it is!
That was a crazy game, huh? If the players got used to the terms, it would be a lot more concise. And you probably could get to the point where you don't need any "like a...[actual object]" phrases. Because the whole point is to NOT say "it looks like a ....". The whole point is to construct the thing in someone's head without any reference to real-life objects. (I guess geometrical objects are still a reference to SOMETHING, but...)
In this exercise, obviously the object was a real object in the real world, but like I said in the introduction, it would be interesting (and more challenging) if the object was abstract.
I guess the point of the whole thing is more of a commentary on language. I wonder if aliens have a way of communicating where they could tell the other person more concisely exactly what some complicated object looks like. Like, they'd be able to "beam" the whole in-out-over-and-under schematic to the other guy, and he'd be able to imagine it instantly.
Assuming you limit the vocabulary to all geometric shapes, it's basically the same thing is 3-D modeling on the computer. Only it's probably even more annoying.