Polyhedron
Polyhedrons are 3D solids with flat polygonal faces, straight edges, and vertices.
It is derived from the Greek word, where 'poly' means "many" and hedron means "surface".
Sort the following objects into two groups: polyhedrons and non-polyhedrons based on their basic properties.
Observe the polyhedrons that you have sorted above. What do all the objects have in common regarding their vertices, edges, and faces? Is there a mathematical relationship that works for every solid?
Regular vs Irregular Polyhedron
A solid is classified as regular if and only if it meets all three criteria for regularity:
- Face regularity - All faces must be congruent regular polygons.
- Vertex regularity - The same number of faces must meet at every vertex in exactly the same arrangement
- Convexity - The solid must be convex.
Convex versus Concave Polyhedron
A convex or concave polyhedron is similar to the concept of a convex or concave polygon.
The test:
Select two points on the surface of a polyhedron.
Form a line segment.
If the line segment joining the two points on the surface of a polyhedron lies entirely inside the polyhedron, it is called a convex polyhedron.
If a line segment joining any two points on the surface of a polyhedron goes outside the polyhedron, it is called a concave polyhedron.
Try out using the solids above.
Tip: Select two farthest points of a solid
1. Analyse the regularity and convexity of following polyhedron.
2. Analyse the regularity and convexity of following polyhedron.
3. Analyse the regularity and convexity of following polyhedron.
4. Analyse the regularity and convexity of following polyhedron.
5. Analyse the regularity and convexity of following polyhedron.
