I’m fairly sure that the 4-colour rhombohedral lattice contains the tesseract. A Google search for tesseract images led me to the following very interesting web page:
http://members.shaw.ca/johnhendricksmath/tesseracts.htm
Tag Archives: 4-color lattice
Kissing Number
I found a great link this morning on Mathworld.com, a piece about the Kissing number. This is twelve in 3-D and 24 in 4-D. I wonder if I can explain 24 for 4-D on the four colour rhombohedral lattice.
http://mathworld.wolfram.com/KissingNumber.html