Math CentralQuandaries & Queries


Question from dawn, a parent:

which solid figure has 4 more edges than vertices?


There are many but I'm guessing that you mean a regular solid (all the edges are of the same length and the number of edges as each vertex is the same). The cube has 8 vertices, 12 edges and 6 faces.

In general for solids the following is always true:

#vertices - # edges + #faces = 2.

In the cube you'll notice this gives 8 - 12 + 6 = 2. This relationship was discovered by the Swiss mathematician Leonhard Euler (pronounced Oiler) in the 18th century. So when you have a question like yours then you know #faces = 2 - # vertices + #edges, i.e., in your case, #faces = 2 +4 = 6, so you have the cube.



About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS