As shown below, four tiles, each with one corner cut, with an inset in the cut-out center, form the center diamond design.

12 X 12 X .5 Flat 6 inch **Corner Cut** Concrete or Plaster Tile Mold
Item # CON-092
With a combination of 4 of these tiles and one of our 6 inch tiles made in our 6" X 6" X 1/2" Concrete Tile Molds. Using this pre-formed cut corner saves a huge amount of labor to make the **center diamond design.**
http://www.moldwarehouse.com/flat_6x_corner_cut_tile.html

Florida Tile is now offering CornerStones. The three colors of beautifully clefted 13”x13” floor tile or 13"x13" **with a cut corner.** The cut tile will accommodate any of the stunning variety of 2x2’s from our many exciting lines such as the gorgeous glass inserts from VitraArt, the bold and stylish metal pieces from MetalArt or our Perfect Partners to mention just a few. Take your floors to a new level of style.
http://www.floridatile.com/ProductStuff/Cornerstones.htm

Inset Tile:A tile with a different design than the surrounding body of tiles.
http://www.artisansofthevalley.com/comm_gloss3.html

Insert - Tozzetto (it) - Taco (sp) - Small decorative tiles used in combination with larger or plain tiles to create patterns. Small square inserts are known as insets.
http://www.iberiatiles.com/PagesProducts/TechTerms.htm

Natural materials are used throughout the room to create the spa-like environment that the homeowners wanted. **The corners are cut from large field tiles, creating square insets when the tiles are placed on a diagonal. The insets are filled with the same small mosaic tiles as the ones used in the tile rug.** The subtle color of the walls creates a beautiful backdrop, and the diagonal layout makes the eye go outward to create the illusion of more space.
http://www.hgtv.com/hgtv/dc_design_bathroom/article/0,1793,H...


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Note added at 10 hrs (2007-10-05 04:19:33 GMT)
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In the following example, instead of four ceramic tiles with a corner cut, the wood is laid to form four squares, each with one corner cut, for the insertion of the ceramic tile square which is to serve as the center diamond.

In Image 1, a 2-inch-square ceramic tile is installed 45 degrees off-center **(diamond style)** in the middle of the room, and surrounded by a hardwood floor. The room is 12-feet-by-12-feet, with a ¾-inch plywood subfloor. The hardwood flooring is unfinished, ¾-inch thick, 2 ¼-inch wide, select red oak. The medallion is made of four, 12-inch-square, hand-painted ceramic tiles, ¼-inch thick. Since the ends of the hardwood flooring abut the secondary material, the flooring will have a “fanning” effect as it works out from the medallion.
http://www.fcimag.com/CDA/Archives/7327515abb0d8010VgnVCM100...


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Note added at 22 hrs (2007-10-05 16:31:25 GMT) Post-grading
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You're welcome, Carol, and thank you! and I really like how you rephrased it for the glossary entry :-)