Complete the table and calculate F - E + V for each geometric solid. What do you notice? Look at Euler's formula. This equation shows us the number of vertices, faces and edges 8−7+1=2. Is this a polyhedron. Why or why not?

Here is the completed table:

Solid	Vertices (V)	Edges (E)	Faces (F)	Calculate F - E + V
Triangular prism	6	9	5	$5 - 9 + 6 = 2$
Rectangular prism	8	12	6	$6 - 12 + 8 = 2$
Pentagonal prism	10	15	7	$7 - 15 + 10 = 2$
Hexagonal prism	12	18	8	$8 - 18 + 12 = 2$
Octagonal prism	16	24	10	$10 - 24 + 16 = 2$
Triangular pyramid	4	6	4	$4 - 6 + 4 = 2$
Square pyramid	5	8	5	$5 - 8 + 5 = 2$
Pentagonal pyramid	6	10	6	$6 - 10 + 6 = 2$
Hexagonal pyramid	7	12	7	$7 - 12 + 7 = 2$
Octagonal pyramid	9	16	9	$9 - 16 + 9 = 2$

What do you notice?
For all the polyhedra in the table, the calculation $F - E + V$ always equals 2. This is known as Euler's formula for polyhedra.

Problem solving:
Look at Euler's formula. This equation shows us the number of vertices, faces and edges $8 - 7 + 1 = 2$. Is this a polyhedron? Why or why not?

No, this is not a polyhedron.
A polyhedron must have at least 4 vertices. The given values (F=8, E=7, V=1) imply only 1 vertex, which is not possible for a polyhedron. A solid with only one vertex is typically a cone, which is not a polyhedron because it has a curved surface, not flat faces.