I understand that the shadow of an object is one dimension less than the original object.

What what the shadow of a tesseract look like? Are there any real world examples?

Edit:

I found this, the Grande Arche in Paris which is a hypercube. Is this a true tesseract, and does it have a 3D shadow?

• I don't remember how the base of Grande Arche looks like. The other part of it does look like the projection of a tesseract into $\mathbb{R}^3$ along one of its symmetry axis. Along a general axis, the shadow/projection (either orthographic or perspective) of tesseract is something like what is shown in this video. May 8, 2014 at 7:20

Undestanding "shadow" as projection, see at Wolfram:

http://mathworld.wolfram.com/Tesseract.html

and many other sites:

http://slumathcsclub.wordpress.com/2011/10/24/4-dimensional-hypercubes/

• Presumably that's what is meant, but physically the identification of "shadow" as projection is doubtful since light propagates in $3$ dimensions, not $4$. May 7, 2014 at 7:03
• @RobertIsrael, interesting twist. But why the restriction on the 4D-light in the 4D space? May 7, 2014 at 7:17