Platonic Solids
Definition
Definition
A platonic solid is a regular convex polyhedron.
A platonic solid is a regular convex polyhedron.
For a regular polyhedron:
For a regular polyhedron:
- All faces are congruent regular polygons.
- Same number of faces adjacent to each vertex.
- Dihedral angle (Angle between 2 planes) are equal between each face.
Explore!
Explore!
Use the applet below to explore the properties of the 5 Platonic Solids.
Use the applet below to explore the properties of the 5 Platonic Solids.
Can you prove that there are only 5 possible platonic solids?
Can you prove that there are only 5 possible platonic solids?
Hint! The angle defect for polygons around each vertex must be positive in order for the polyhedral net to fold into a polyhedron.
Hint! The angle defect for polygons around each vertex must be positive in order for the polyhedral net to fold into a polyhedron.
Next: You can unfold the nets of the 5 platonic solids here.
Next: You can unfold the nets of the 5 platonic solids here.