Abstract
This paper proposes a definition of vertexes, edges, and faces (VEF) suitable for high
school students, modifying its essential definition in topology. The paper describes difficulties
in finding a proper definition of VEF, and the detailed process of revising the definition. In our
previous lesson on Euler’s formula for polyhedron in a high school, students were confused to
count the number of VEF of a torus. This confusion came from the fact that they were seized
with the meaning of VEF in school mathematics. We tried to define VEF as terms in everyday
use, which represent essential meanings in topology.
