Cordoba Tiles – 30 STEM Links a Week

SketchUp is a free and fun program for 3D modeling. You can use SketchUp to design just about anything, from furniture to a dream bedroom to an entire city.

There is a downloadable version called SketchUp Make, as well as a web-based version which works right in your Internet browser. This version is called my.sketchup, and to use it just go to www.my.sketchup.com.

Now for the project.

A long time ago I bought this great book by Eric Broug, on constructing Islamic tiles:

Some of the geometric constructions in this book are quite complex, but most are pretty easy to do in SketchUp. This project comes from the first construction in the book: tiles from the Great Mosque of Cordoba in Spain.

The interior of this famous mosque looks like this:

And the tiling pattern we’ll create (though not with this much detail!) is found in several spots, including on this floor in the courtyard:

Here’s how to make this in SketchUp.

After you go to the SketchUp page and launch your modeling session, here’s what you should see: a man (Josh) standing on the ground with axis lines around him. The red and green axes are on the ground, blue is for the vertical direction.

We don’t want Josh standing on our tiles, so click the Eraser icon or press the E shortcut key.

Click on any edge of Josh to erase him.

Since the tiles will be drawn on the “ground,” we need to switch to a bird’s eye view – looking down on the ground from above. On the right side of the window, click the Views icon.

Click the icon that looks like the top of a house.

You should now be looking straight down onto the red – green plane.

Press R for the Rectangle tool, and click to place the first corner anywhere. Don’t keep your mouse button pressed – no dragging. Then move your mouse in any diagonal direction until you see the “Square” popup, and click again for the second corner.

The next object to draw is a circle that’s perfectly centered in the square. First, press C for the Circle tool. Then hover (don’t click) on any midpoint of any edge of the square. And then hover over any midpoint of an adjacent edge.

Move your mouse to the center of the square, and when you’re in the exact right spot, you’ll see dotted lines from the two midpoints where you were hovering. When you see those dotted lines, click to place the circle center.

For the second point of the circle, click on any midpoint of the square.

Now we can use the circle and square to construct the rest of the Cordoba Tile.

Press L for the Line tool. Start the line at any rectangle corner, and end the line at the center of the circle.

Now add the two lines shown below, each starting at the point where the line and circle intersect, and ending where the circle meets the square. Be sure to click on intersection points and endpoints – drawing “by eye” won’t be exact enough.

For these two diagonal lines, each needs to be extended to meet the edges near the corner of the square. Which is easier than it sounds. Start the line where the diagonal line meets the circle, and move your mouse so that the preview line is magenta. This means the line will be following the same direction as one of the existing lines. End the line when it meets the correct edge of the square.

Do the same to extend the other diagonal line.

These are all the lines we need to complete the construction. Now we need to rotate-copy what we’ve just made. Start by pressing Ctrl + A (PC) or Cmd + A (Mac) to select everything in the model. All edges and faces should be highlighted in blue.

Press Q to activate the Rotate tool. The first step with Rotate is to place the protractor at the center of rotation, which is the center of the circle.

The next two clicks determine the rotation angle. But first, press the Ctrl key (PC) or Option key (Mac). This adds a plus sign to your cursor, meaning a copy will be created. (You don’t have to keep this key pressed, just tap it.) Then click any corner of the square.

For the end of rotation, click any adjacent corner of the square. The Angle field in the lower right corner should say 90 degrees.

This created one rotated copy, but we need rotated copies in the other corners as well. In other words, we need three total copies, not just one. To get these copies, type 3x (which appears in the Angle field), then press Enter. Don’t place your cursor in the field, just type and the characters will appear. Now the square should have the same sets of lines in all four corners.

Click anywhere in blank space, to unselected everything.

Now we have to erase some lines of this construction. Start by erasing the short lines in the four corners.

Then erase the lines that divide the eight diamond shapes that surround the center.

Finally, erase everything inside the 8-pointed star in the center, and erase all the parts of the circle as well. You might have some faces disappear, and some lines that should be thin may appear bold.

If you have any holes, or bold edges in the middle, activate Line and trace over any of these edges. What you should have is this: no holes and all thin lines in the middle. The only bold edges should be the outer edges of the square. This square and its lines make up the Cordoba Tile.

Now for the fun part: painting and copying. Click this icon to open the Materials window.

To look through the various material options, click the Browse icon. The list of categories includes Colors, as well as a variety of textures.

In my example, I used solid colors to get this:

(If you try to paint a face and the color remains gray, you may have double faces. These aren’t supposed to exist in SketchUp but sometimes there are bugs. If this happens, press the Spacebar, click the face to select it, and press the Delete key. There should be another face just below, and that one should be paintable.)

Because the pattern can only be seen when the tile repeats, the tile should be made into a component. To make the component, press Ctrl + A or Cmd + A again to select everything. Right-click on any selected face and choose Make Component.

Give the component any name, or keep the default name. You can ignore the other options, and click OK.

Now this tile is a single object, rather than a set of loose edges and faces. This makes it much easier to make copies, changes, etc.

To make the copies, press M for the Move tool. Tap the Ctrl or Option key for Copy mode. Copying is done with two clicks: start and end. Click on the two endpoints shown below to place the first copy.

Then type 2x (or 3x or whatever number you like) to make additional copies.

For the copies in the other direction, do the same steps: Select everything, make the first copy in the vertical direction, then increase the copies.

We’ll now hide edges, to make the pattern easier to see (and prettier).

The beauty of using components is that if you make changes to any component, all other components get the same changes. Right-click on any tile and choose Edit Component. (You can also press the Spacebar for the Select tool and double-click a component to edit it.)

The component that’s now open for editing is now surrounded by a dotted-line box, and everything else is faded in the background. This means that only what’s inside the component can be changed, everything else is off-limits. Activate Eraser, press and hold the Shift key, and click all outside edges of the square to hide them.

When finished, right-click in blank space and choose Close Component. (Or press the Spacebar and click anywhere outside the component.)

Here’s my new pattern, with all horizontal and vertical edges hidden.

You can continue making changes each time you edit a component. For example, you can change colors of any of the shapes.

Or, if you’re good at using the Offset tool, you can even make something like this:

What patterns can you come up with?

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