Thread: Number of Vertices from Polyhedron

Hi there,

i have an arbitrary, closed polyhedron that consists of n triangles. Can I find out the number of vertices only with this given information? Thx.

Originally Posted by dpdp

Hi there,

i have an arbitrary, closed polyhedron that consists of n triangles. Can I find out the number of vertices only with this given information? Thx.

Yes. Each triangular face has three edges, and each edge is shared by two faces. So if there are n faces then there are 3n/2 edges. You can then use Euler's formula to find the number of vertices.