No. The figureis madeup of polygonsand it has faces,edges,and vertices.But the facesdo not fit to-
gether—thefigurehas gaps.The figurealso has an overlapthat createsa concavesurface.For thesereasons,
the figureis not a polyhedron.
Face,Vertex,Edge,Base
As indicatedabove,a polyhedronjoinsfacestogetheralongedges,and edgestogetherat vertices.The
followingstatementsare true of any polyhedron:
- Eachedgejoins exactlytwo faces.
- Eachedgejoins exactlytwo vertices.
To see why this is true, take a look at this prism.Eachof its edgesjoins two facesalonga singleline segment.
Eachof its edgesincludesexactlytwo vertices.
Let’s countthe numberof faces,edges,and verticesin a few typicalpolyhedra.The squarepyramidgets
its namefrom its base,whichis a square.It has 5 faces,8 edges,and 5 vertices.
Otherfigureshavea differentnumberof faces,edges,and vertices.