6 Ways to Build a Cube

[size=150]Illustrated below are 6 possible ways students can construct a cube in [url=https://www.geogebra.org/3d]GeoGebra 3D Calculator[/url]. [br]There are other ways as well. [br][br]Of course, some methods are more suitable for students studying 3D geometry concepts for the first time (like methods 1, 2, 3). For others, we can make it more of a challenge that prompts them to use concepts they're studying in higher level courses (3D coordinate geometry, geometric transformations, compass-and straightedge constructions as shown in methods 4, 5, & 6, respectively). [/size]

METHOD 1: Use the CUBE tool. Select the CUBE tool, plot 2 points, and YES, it's that easy!

METHOD 2: Use the REGULAR POLYGON tool to first create a square base. Then, use the CUBE tool applied on this square. Yes, it's that easy!

METHOD 3: Use the REGULAR POLYGON and EXTRUDE TO PRISM tools

METHOD 4 (Coordinate Geometry Approach): Plot 8 possible vertices (x, y, z) and use the POLYGON tool to construct each of its faces.

METHOD 5: Use the REGULAR POLYGON tool to create a square base. Then use the VECTOR and TRANSLATE BY VECTOR tools to construct its other 5 faces.

METHOD 6: (Compass and Straightedge Method): Use the LINE, RAY, and CIRCLE WITH CENTER, RADIUS, & DIRECTION, and INTERSECT tools to construct 2 of the cube's faces. One face is on the gray plane and the other is in mid-air. Then use the VECTOR and TRANS