Sometimes i seem to be in need of a folded paper-like text, so I thought I'd give it a try and simulate this in Adobe Illustrator. You'll be able to use this either for a folded paper logo design or for other design work. We will use only Illustrator to create a text that will look like built using folded strips of paper.
Open a blank Illustrator file and type FOLD in a black bold font. We are going to use this as a mere guideline for our folded text size and proportions.
Use the rectangle tool and create a rectangle like in the image. We are going to use this as a base for our letters. We need to keep in mind that for a folded style typography the letters need to have the same thickness for all the sides.
Use transparent for the rectangle fill and red for the outline so that it is easier to follow the changes. Duplicate the rectangle and rotate 90 degrees and adjust the length to create the horizontal parts of the letter F.
With the FOLD word as guideline create the letters using the rectangles like in the image. Take the FOLD word aside, fill the resulting shapes with a grey color and you should have something like this.
Drag some guidelines to help you and start cutting the shape's corners like in the image. Do not weld the images as we will need them separately later. Cut the corners of our future letters like in the image and fill the resulting shapes with a blue color.
Select the parts of the letters that will go in the back plan and fill it with a lighter blue color.
Duplicate (copy and the paste in place) the vertical part of the letter F and fill it with white color for the moment. We will use this to create some lighting to give the folded letter a bit more dimension.
Fill the vertical part of the letter F in the foreground with a vertical gradient white to transparent and then set transparency to 50%.
Use the same technique for the vertical element of letter L and the horizontal elements of letter D.
For the letter O, duplicate the horizontal elements and use a gradient fill white to transparent to white and then set transparency of the elements to 50%.
Duplicate the elements that will go in the background and fill them with black for the moment.
Fill the duplicated horizontal elements of letter F and L with a horizontal gradient fill black to transparent, set blending mode to multiply and transparency to 50%.
Fill the duplicated vertical elements of letters O and D with vertical gradient fill black to transparent to black, set blending mode to multiply and transparency to 50%.
For the final version I've increased the transparency of the duplicated background elements to 70% to have more contrast. Here you have your folded text that you could use for a folded paper logo design and you have many creative tips that you could apply in various design projects.