Maximizing Surface Area: Open Middle Cube Problem (V2)

Creation of this resource was inspired by an [url=https://www.openmiddle.com/]Open Middle[/url] problem by [url=https://twitter.com/DrBrianLack?lang=en]Dr. Brian Lack[/url]. [br][br][br]The prism below is made up of 27 identical cubes. [br]You can drag the white points to move any cube away from the large main cube. [br]Dragging a white point will move it left or right. [br]Click on any white point and then drag it to move it up or down. Click on the point again to then drag it left or right.
What is the greatest possible surface area this surface can have after removing 1 or more cubes from this giant cube? Explore!
What is the greatest possible surface area this surface can have after removing 1 or more cubes from this giant cube? Explain what you found below.
For an AR-friendly version of the app above, [url=https://www.geogebra.org/3d/zz4jxzfv]open this[/url] in GeoGebra 3D Calculator on your phone or tablet.
Quick Silent Demo in AR
– Tim Brzezinski, IM 6 – 8 Math

Information: Maximizing Surface Area: Open Middle Cube Problem (V2)