Although polyhedra are generally named by the number of faces that make up the figure, it is common to see qualifier of the face shape within the name.
Likewise, in naming threedimensional figures that are not regular polyhedron, it is critical to know the shape of the base. The name of the shape of the base will be used in naming the solid and the net of the solid.
Euler’s Theorem tells us the relationship between the number of faces, edges, and vertices in any polyhedron. Remember that a polyhedron is a threedimensional figure whose faces are all polygons, and polygons are planar shapes with closed edges and no curved edges.
Source: Leonhard Euler, Jakob Emmanuel Handmann, Wikimedia Commons
Will Euler’s Theorem still apply to a polyhedron that is not regular?
Look at the table below to see information about each polyhedron.
Name of Shape 
Number of Vertices 
Number of Faces 
Number of Edges 
Check
V+F – E = 2 
Pentagonal Prism 
10

7

15

10 + 7 – 15 = 2 
Triangular Prism 
6

5

9

6 + 5 – 9 = 2 
Pentagonal Prism 
6

6

10

6 + 6 – 10 = 2 
Conclusion Questions
 Why do you think Euler’s Theorem still applies to polyhedra that are not regular?
 To what nets of threedimensional figures, if any, will Euler’s Theorem not apply?