Polyhedra, Nets and Schlegel Diagrams
This is a net of
pentagonal
pyramid.
A polyhedron (plural polyhedra or polyhedrons) is a
solid in three dimensions with flat polygonal faces,
straight edges and sharp corners or vertices.
A Schlegel diagram is a 2
dimensions network
representing a polyhedron.
This is a Schlegel
diagram of pentagonal
pyramid.
The net of a polyhedron is an arrangement of edgejoined polygons, which can be folded (along edges)
to become the faces of the polyhedron.
Sketch the net of a triangular prism
This is a
pentagonal
pyramid.
This polyhedron has
10 edges, 6 vertices
and 6 faces.
Euler found the following relationship:
F + V – E= 2
Check this is true for the pentagonal pyramid and
triangular prism
A Schlegel diagram can be made from a polyhedron by
firstly removing a single face. This edges of this face
form the outside of the diagram. Then the arrangement of
vertices and edges that can be viewed inside the polyhedron form the interior of the Schlegel diagram.
Platonic Solids
How many
faces, edges
and vertices
does this
prism have?
Here is some research for you to do:

What is a Platonic Solid?

How many Platonic Solids are there?

Name the Platonic Solids?

What is the net for each Platonic Solids?

What is the Schlegel diagram for each Platonic
solid?

Does Euler’s Relation apply to each Platonic solid?
Draw the Schlegel Diagram for a
triangular prism by:

removing a triangular face

removing a rectangular face