# Bogglers

By Scott Kim|Tuesday, April 01, 2003

Mind-Bending Shapes
Geometric forms abound in the sculptures and drawings of pioneering conceptual artist Sol LeWitt. His systematic and playful arrangements of shapes often embody visual riddles, so we've devised a series of exercises, based on LeWitt's artwork, for you to wrap your mind around. Cubes Each of the 122 sculptures in LeWitt's Variations of Incomplete Open Cubes is a shape with a series of contiguous lines using at least three— but not more than 11— of the edges of a cube. Sixteen possible variations appear in the diagram above, with each two-dimensional rendering representing a three-dimensional structure. Figure 4 of the diagram, for instance, represents the shape at right. Lines that appear to meet at the center of a figure in the diagram do not necessarily meet in the actual three-dimensional figure. 1. [Easy] The first three figures in the diagram show all the incomplete open cubes you can make with just three edges. Can you make six different shapes that each contain four edges? The edges in each shape must all connect to form a single figure. Mirror images of the same shape are considered different, but rotations are not.

2. [Challenging] Which pairs of figures represent mirror images and/or rotated versions of the same three-dimensional shape? Hint: Only two are not part of mirror-image or rotation pairs.

3. [Difficult] How many distinct shapes can you make using five connected edges of a cube? Again, mirror images of the same shape are considered different, but rotations are not. Arcs The diagram above is based on LeWitt's Wall Drawing #358. In this work, each square tile contains a quarter arc in one of four possible orientations.

1. [Easy] By joining two adjacent tiles, you can make a "domino"— a two-part figure containing two of the quarter arcs. Which domino occurs four times in this figure, either horizontally or vertically? A single square may be used in two separate dominoes, and dominoes may be rotated. The two dominoes below, for example, are considered the same: 