A tesseract is a 4regular graph with 16 vertices If it was p

A tesseract is a 4-regular graph with 16 vertices. If it was planar, it would have a simple regular dual. From what we know about Platonic Solids, could the Tesseract be a planar graph? Please look up what it looks like! If a cube comes after a square, then a tesseract comes after a cube.

Solution

Tessaract is not a planar graph.

In terms of Plataonic solids, V-E+F=2 , by Euler.

In this case, a Tessaract will have 8 faces, but V-E+F= 16-(16x4/2) +8 = -8 is not equal to 2.