The northern section of El Paso County known as the Tri-Lakes region appears to be an epicenter of a significant housing boom. Shannon Bingham, owner of Western Demographics, estimates that 2,350 new homes will be built in the area by 2024, with the majority being completed in the coming four years.
We use these relationships to derive the general formula for polygonal numbers. In finding the number of dots in a polygon, two quantities vary. The first varying quantity is the number of sides of the polygon which we have denoted above as n. The second quantity is the size of the polygon which we denote as k.
We're now ready to see what Euler's formula tells us about polyhedra. Look at a polyhedron, for example the cube or the icosahedron above, count the number of vertices it has, and call this number V. The cube, for example, has 8 vertices, so V = 8. Next, count the number of edges the polyhedron has, and call this number E. The cube has 12 edges, so in the case of the cube E = 12. Finally, count the number of faces and call it F. In the case of the cube, F = 6. Now Euler's formula tells us that.