Polyhedra – Bases, Faces,
Edges, and Vertices
3/10/16
What is a polyhedron?
• A three-dimensional figure with faces that are
polygons.
• These are all polyhedra:
What is a face?
• Hint: It’s not on your head!
• Any flat surface of a polyhedron
Face
Face
Face
What is a vertex?
• The point where three or more faces of a
polyhedron intersect
Vertex
Vertex
Vertex
What is an edge?
• An edge connects two vertices and is where two
faces meet
Edge
Edge
Edge
How many faces, edges, and
vertices does this cube have?
• Faces:
6 faces
• Edges:
12 edges
• Vertices:
8 vertices
What is this shape called?
• Prism:
• A three-dimensional figure with
at least three rectangular lateral
(the sides) faces and two
parallel bases
• Base:
• The bottom and/or top of a
polyhedron. If there are two
bases, they will be parallel to
one another.
What specifically is this shape
called?
• A rectangular prism:
• We know it’s a prism because its
sides are rectangles. It’s a
rectangular prism because the
bases are rectangles.
What types of prisms are these?
• Triangular prism:
• The sides are
rectangles and the
bases are triangles
• Hexagonal prism:
• The sides are
rectangles and the
bases are hexagons
Find the number of faces,
vertices, and edges.
• Faces: 5
• Edges: 9
• Vertices: 6
• Faces: 8
• Edges: 18
• Vertices: 12
What is this shape called?
• Pyramid:
• A polyhedron with one
base and three or more
triangular faces that meet
at a vertex.
• Specifically this is a
rectangular pyramid
because the base is a
rectangle.
What type of shape is this?
• Cylinder:
• A three-dimensional figure
with two parallel circular
bases connected by a curved
surface
• How many faces, edges,
and vertices?
• Faces: 2
• Edges: 0
• Vertices: 0
What type of shape is this?
• Cone:
• A three-dimensional figure with
one circular base connected by a
smooth curved surface to a
single vertex.
• How many faces, edges, and
vertices does a cone have?
• Face: 1
• Edges: 0
• Vertices: 1