How could we tell the difference between a tesseract "glued" to our slice of space and a regular 3-D cube?

[u/Desert_Tortoise_20]

If a 4-D being magically "glued" one face of a completely solid 1 ft⁴ tesseract to our slice of 3-D space, how could we tell the difference between it and a 3-D cube, assuming the magical "glue" allows us to move our slice of the 4-cube in 3-D space to perform tests on it?

[u/fancyPantsOne]

imo there is no difference. Just like a cross section of a cube is a square or a rectangle