The pictures above show patterns for the lettering on the Klein Bottle and Projective Plane hats. They are designed assuming you work a tube with the inside of the tube facing you. The patterns are designed to be read from right to left and bottom to top (the same way you would knit them). If knitting the Klein Bottle, begin the pattern after knitting 8 inches of the hat at the full width (88 sts wide in my case). If knitting the Projective Plane, begin the pattern when the total length of the hat is about 13 inches.

If you're working the Klein Bottle:
Begin by taking a second piece of your primary color yarn long enough to work one row, and work one row with both yarns together (so you'll end up with twice as many stitches on the needle). Keep the second piece of yarn on the front side (inside of the tube). For the next two rows, you'll be working two layers at once. Use your secondary color for the front layer, and your primary color for the back layer. The next 7 rows will form the lettering. At each of the squares marked with an "x", switch colors and work a purl stitch with the secondary color (even if the current stitch would normally be a knit). Also make the same stitch in the next row a purl stitch, but this time don't switch yarn colors. This will make all the stitches that form the lettering look the same. I've written little P's in the pattern to remind you to do this. Skip past the Projective Plane paragraph for the rest of the instructions.

If you're working the Projective Plane:
Begin by taking a second piece of your primary color yarn long enough to work one row, and work one row with both yarns together (so you'll end up with twice as many stitches on the needle). Keep the second piece of yarn on the back side (outside of the tube). For the next two rows, you'll be working two layers at once. Use your secondary color for the back layer, and your primary color for the front layer. The next 7 rows will form the lettering. At each of the squares marked with an "x", switch colors and work a knit stitch with the secondary color (even if the current stitch would normally be a purl). Also make the same stitch in the next row a knit stitch, but this time don't switch yarn colors. This will make all the stitches that form the lettering look the same. I've written little K's in the pattern to remind you to do this. The letters will show on the inside of the tube, but don't worry, the projective plane pattern will have you invert the hat so the letters end up on the outside in the end.

When you're done with the lettering, work two more rows with both colors, then replace the secondary color yarn with a piece of your primary color yarn long enough to make at least one row with. After knitting one row with the two strands being the same color, combine the two layers back into one using k2tog and p2tog. Continue knitting the hat normally according to the instructions.
Back to Knitting One Sided Surfaces

DISCLAIMER: THIS PAGE IS NOT A PUBLICATION OF THE GEORGIA INSTITUTE OF TECHNOLOGY AND THE GEORGIA INSTITUTE OF TECHNOLOGY HAS NOT EDITED OR EXAMINED THE CONTENT. THE AUTHOR(S) OF THE PAGE ARE SOLELY RESPONSIBLE FOR THE CONTENT.