The 2x2x3 "Slim Tower" is a cube type transformation using a standard 3x3x3 57mm Rubik's Cube and a 30mm keychain 3x3x3 Cube. The raw materials to make the Slim Tower are purchased directly from rubiks.com. The Slim Tower's dimensions are 38mm x 38mm x 57mm. See the above image for a direct comparison between a standard Rubik's Cube and the Slim Tower.
The general principle for making a Slim Tower is explained in the Tony Fisher's Cuboid 3x3x3 Transformations section of twistypuzzles.com. A useful tutorial for creating one can be found at Ton Dennenbroek's excellent web page. My approach is very similar to Ton's method except I have standardized the creation process a bit to help reduce the hours necessary to make a Slim Tower. The end result is a consistent, repeatable product that feels tightly put together and turns smoothly.
Cost for a standard Slim Tower in black or white plastic is $80 in US dollars. The price includes shipping worldwide. You may specify a sticker color pattern if you so choose. Otherwise it will get the standard official Rubik's Cube pattern as shown on this page.