Sandpaper is an interesting medium for origami. Although it can be hard on the fingers, sandpaper provides some interesting tactile and visual textural variations, is very durable (often waterproof), and has a grit which facilitates interlocking of multiunit assemblies by increasing friction between the pieces.
The above shape is a truncated stellated icosahedron, meaning that it is derived from the regular 20-sided polyhedron (the icosahedron) by projecting triangular pyramids (stella) from each of the faces and then truncating the stella (i.e. lopping them off). It is taken from Tomoko Fuse's excellent book, Unit Origami: Multidimensional Transformations, being constructed from 30 identical "little turtle" units as described on pp. 56-57 of the book's first edition. Each unit is folded from a square of 3M 130N garnet C-weight open coat sandpaper. The entire assembly is held together by friction only, and measures about 6" across. It was folded and constructed with the assistance of Melody Klingler.
This square box (with "Pinwheel" lid) is taken from Tomoko Fuse's Origami Boxes. It is folded from four squares of 3M 431Q 180 grit Wetordry C-weight Tri-M-ite sandpaper (the dark color), and four squares Norton 120 grit P-grade A-weight sandpaper (the light color). The sandpaper causes enough friction between the lid and sides of the box that the lid will stay in place even if the box is inverted and shaken, although it is easily removed by hand.
This "Temari ball" is taken from pp. 68-69 of the first edition of 3D Origami (ISBN#:4889960570). It is constructed from 256 identically-folded 3" squares of sandpaper: 110 of generic 600 grit A-weight waterproof sandpaper (dark pieces) and 146 of Norton 150 grit BL sandpaper (light pieces). The finished ball is about 4" tall and 3" across and is extremely sturdy.
Probably the least successful of all my sandpaper origami projects has been the triceratops. When I was first thinking of unique applications of folded sandpaper, it occurred to me that the harsh texture of the very-low-grit sandpapers (60-100 grit) might give the impression of "rough hide" in a model of an animal like an elephant or an alligator or a dinosaur. The problem, I quickly realized, is that the heavier sandpapers are also much more difficult to fold, making complex models essentially impossible. So the problem was to find a simple model of an animal with rough hide. I found and attempted several elephants, but these either lacked verisimilitude or were too complex to fold in the heavy paper. Another problem was that many eligibile models displayed the reverse side of the paper, which in most sandpapers is of strikingly different coloration that the grit side. I finally settled on this triceratops, which was designed by Javier Caboblanco and published in the Origami USA Annual Collection 1999 (pp. 54-55). (I first ordered this photocopied ring-bound collection from the Origami USA website because it contains instructions for Herman Van Goubergen's remarkable Skull.) The model shown here is folded from three 9" squares of Norton 3X 60-grit sandpaper. Folds do not stay well in this heavy blue paper, and some parts of the model had to be glued. Also, because the paper is so heavy, the head of the triceratops, which is a separate sheet, had to be glued in its upright position; otherwise it tended to slide down until it was resting on the ground. The finished triceratops is about 12" long.