Question

Use what you know about the number of faces, vertices, and edges in polyhedrons to choose True or False for each statement.

A. A triangular pyramid has the same number of faces as vertices. True or False
B. A triangular prism has the same number of faces as vertices. True or False
C. The sum of the faces and vertices for a triangular prism is 11. True or False
D. The number of edges of a polyhedron is 2 less than the sum of the number of faces and vertices. True or False

Answer 1

A. True

A triangular pyramid has 4 faces and 4 vertices.

B. False

A triangular prism has 5 faces and 6 vertices.

C. True

Since the number of faces is 5 and vertices is 6 then the sum will be equal to 11.

D. True

Any convex polyhedron's surface has Euler characteristic − + =, where V is the number of vertices, E is the number of edges, and F is the number of faces. This equation is known as Euler's polyhedron formula. Thus the number of edges is 2 less than the sum of the numbers of vertices and faces.