Illustrated below are 6 possible ways students can construct a cube in GeoGebra 3D Calculator.
There are other ways as well.
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).
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